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2026 StatenNaturenDel4¦2b: 27Aug ♦ Del3¦2a Juni: IPCC AGW — Del2 Maj: Rotvältor, Sverige — Del1 Mars: Rotvältor, Lokalt — Ansvarslös statsförvaltning ¦ Physics 7 Applications

Atomkärnans övergripande härledning, beskrivning och bevisning — grunderna för liv, tillvaro och existens: Lagen: Defense

Sections: CWONsynth ♦ TeClaNeaR ♦ ErrorCheck ♦ NeutronBegin ♦ NucDed ♦ ComparingExperimental ♦ Physics7 ♦ NUTGOMAD ♦ NEUTRON ♦ TUNS ♦ TAN26 ♦ RanBam ♦ SAMEXRAM ♦ NKCexplain ♦ RadioMathAug2026 ♦ bHspectrumOrigin ♦ bKOFF ♦ CalCard ♦

CWONsynth: TAN26 ¦ Recognition ¦ Alt3 ¦ AP75 ¦ RelPM ¦

EUROPA 1800+: Statsförvaltningarna ” like-minded ” attackerar mänskligheten.

Kräver öppet lydnad under bestraffningshot. Sverige 2026: ”Gängkriminalitet”.

— Fantastiska förebilder. De12. DeYtterligare26. Sveriges Urkundsförfalskning.

SVERIGES BIBELURKUNDSFÖRFALSKNING.

När ska ett sanningens Ord nå dessa historiskt självutnämnda oanmälda diktaturkräk?

— »Myndigheterna utestänger befolkningarna från kunskapen».

THE Ai MACHINE WORLD PROPAGANDISTIC CONFESSION 1 ¦ THE Ai MACHINE WORLD PROPAGANDISTIC CONFESSION 2 ¦ state/business authority »hijacked humanity» enterprise

World Biological Situation Apr2026+:

A UH summing cosmological comprehensively linked overview ..

Removing natural alive trees, thinning out, of natural forest areas, reduces (Simard2012) the naturally biological strength parameters, reduces long term (thousands of years on a local regional forest site) root established nutrition exchange (Simard2012), and consequently reduces (Simard2012) life power. Only the most excellent ignorant stupid administration can do that.

— Modern Academy 1812+. MLN1812IPCC2013Graph284ppmvCO2.

—The BELOW RIGHT phenomena is apparently a new never before seen extension of the initial spring 2025 last year Bending Trees Phenomena. Original forest areas having been thinned out (only five years back), exposes unnaturally occurring uprooting with fallen trees (Pine, Birch, Aspen .. ). Thinning out also increases through-wind power. In a naturally tight grown forest, the trees support each other by close touching, quickly damping out any hazardous swaying effects. More wind also increases dry ground forest, and thereby supports wildfire.

———————————————

BioEK1-10 ¦ AR123 ¦ Ar1 ¦ CWON — complete whole number solutions: Earth crust composition from 1900s tables ¦

Now if »the most excellent ignorant stupid administration» has got The Attention, let us look at the Picture from a more broad advertising avenue:

Recognition:

———————————————

Recognition

ya, years ago; T t = 10^±: EX: 1T9 ya = 1 G ya, G = Giga = T9.

Earth: AGE in MAC: 4.5 T9 ya; in TNED: 20.8 T9 ya (Voj) — ICE COVER SHELL melting period from primary Earth crust surface heat: 16.2 T9 y: Earth crust mineralogy preparation. In-boiling gas composition: CO2, beginning from Earth primary surface temperature, some 70 000 °C (Temperature-Energy Table).

The RestGAS (ETAB ¦ Rest CO2 @End ¦ 6.390857917 T15 KG carbox) establishes as The (MLN1812IPCC2013Graph284ppmvCO2) natural CYCLIC MLN1812 Biologically Recycling LIFE gas composition. perpetually mixed between Primary Oxygen16 (animal respiration), Carbon12 (decay) and CO2 (Plant respiration), maintaining — untouched — biologically health asserting recycling life to plants and animals through growth and decay on biological respiration (phosphorylation, PO4: mitosis: QUOTES). See StandingCyclicCO2.

During 1800-2000 (ForestWORLD) more than 30% of the natural forest area cover was removed by human hand.

During 200 years. From having worked on building Humans during some 3 billion years.

— And You would not imagine, even, that That would show consequences?

— You were saying?

— Defense .. you name that .. defense .. you said .. ?

MAC:

— Who educated these prominences?

Apparently no Natural Academy.

Alt3: Recognition

Never spotted in MAC:

THE THIRD ALTERNATIVE

DET TREDJE ALTERNATIVET

som aldrig kom fram inom den moderna akademins korridorer, men som ger svaret på hela »den kosmologiska gåtan»:

GENERAL COSMOLOGY — in MAC, ”cosmological principle” (Wikipedia) is a generally academic flourishing term for ”on a large enough scale our universe is homogeneous”.

It is in that concept also included the last academic consensus invented, academically consented, term DARK ENERGY — an observationally spotted ”extra tugging force” on the general observed (Hubble 1920) material expansion of our universe. In related physics and mathematics (TNED) the actual observation is explained by GRAVITATIONAL REDSHIFT, Light’s Gravitational Dependency (LGD ¦ Application P75). Not so explicitly applied in modern corridors, however so conformed only on isolated celestial masses (Mössbauer effect stuff; GPS applications): same math (again, see further examples in EXVER), but on vastly different descriptional basis. The TNED explanation, consequential mathematics, no speculation, no theory, connects as a (final: AllKeplerMATH) proof of the K-cell heat physics (K-cell Expansion, surrounded by »the general c0 body»: Solar Systems in Milky Way), a term of which modern corridor populations also, what we know, are completely unaware.

This is how the subject was presented to, and responded by, the Microsoft Ai CoPilot in Jan2025 (GravitationalRedshift).

EXCERPTS, fully detailed in GravitationalRedshift;

------------------------------------------------------

AP75: Alt3

The Jan2025 New Microsoft Edge Browser’s AI CoPilot answers:

+++++++++++++++++++ MiEcoPilot:

” The exact nature of dark energy is still unknown, but it is often modeled as a cosmological constant or a dynamic field.”.

ApplicationP75

BD1:

..

— Your earlier posts, seem to have confirmed that Relativity Theory is represented in part by the two earlier named mathematical expressions:

— Einstein's form for »Light's Gravitational Dependency» reads:

c/c0 = (1—w²/c²) with w² = GM/r, outside the (spherical mass);

— Schwarzchilds form is (slightly different)

c/c0 = (1—2w²/c0²) with w² = GM/r;

— Now to our crucial »one billion dollar question», testing Your capability (and possibly mine too):

— A Third possible mathematical expression, same subject, is known to have the unique form

c/c0       = (1—w²/cc0);

— Related as "a mass expansion IN space"

— featuring a “Gravitational Redshift” from center to outer;

— IT exposes EXACTLY the same physical instrumental observational Values of Doppler Red Shift, including the Cosmic Background Radiation (CMB) values (2.72548 °K), as claimed by Your earlier stated Theory connected to "an expansion OF space".

— The values are (accurately) the same, but the explaining physics are (diametrically) different:

— Your part:

— Can You confirm or deny THAT this actual third mathematical expression is or is not accurate in claiming concordant Red Shift results with the actually known experimental instrumental observations in our expanding universe?

The Jan2025 New Microsoft Edge Browser’s AI CoPilot answers:

+++++++++++++++++++ MiEcoPilot:

” Yes, I can confirm that the third mathematical expression

c/c0 = (1—w²/cc0)

is accurate in claiming concordant redshift results with the known experimental instrumental observations in our expanding universe.”.

RelPM:

RELATED PHYSICS AND MATHEMATICS bd=h²:

— CheopsRectangle. Application P76.

MAC:

— You were saying .. ?

Disclaim (no offense, just the simple Consequential Mathematical Truth):

Retarded. Low educated. Intellectually disabled. Perfect natural intelligence. A dead end interest in its content and context: no respect.

------------------------------------------------------

LGDbasics ¦ LGDref ¦ c0PRESERVATION ¦ ESR ¦ LGD ¦ SHORTtoLGD ¦ LIGHT’S GRAVITATIONAL DEPENDENCY ¦ LGBvektor ¦ CaseHistory — 2.725 °K — TauKelvinSources ¦ CMBdetails ¦

DEN KOSMISKA BAKGRUNDSSTRÅLNINGEN 2,73 °K, K-cellens värmefysik — Tfaktorn, KcellHeatPhysics

That AP75 ”third mathematical expression” (Application P75) is the (TNED) one derived from Cheops Rectangle bd=h², giving the (c0PRESERVATION) complete deduction of Light’s Gravitational Dependency: all K-cell expansion-contraction consequential mathematics. Really. Never mentioned (yet) in modern corridors. (But it will be, what we know — as MAC:s cosmologically consented walls fall ..).

Initial ICE (TheICE) shell thickness above our present (Req = 6.378 T6 M) Earth spherical ground: 54 KM (present ocean-land-atmosphere water + 19 such mineralogically integrated in Earth’s crust). At the end: one ocean water mass (cracking, 4.3 T9 ya [NASAfactsFirstWater], falling to a still hot surface melt Earth ground; atmospheric oxygen production begins from HESC Earth atmospheric simultaneous Ozone shell production through water vapor and top Atmosphere molecular fragmentation from Sun’s Planck energy hf), with 19 ditto mineralogically ocean-land-atmosphere water masses integrated.

— These figures are the ones we find in the already determined geological measured tabled and general academic references.

— Solar System development. see K-cell Expansion with Earth’s Third Equation and (Dmax) the consequentially related Milky Way Solar Systems mathematics.

BioEK1-10 ¦ TheTEN:

There is no speculation here. No theory. Just consequential mathematics. On observed physics principles. And already sampled geological research during the 1900s.

— It holds — or not at all. Just give the math arguments; Surrender comes unconditional:

THE CONCEPT OF KNOWLEDGE: Analysis(»bePatient» .. research ..) + Insight(»MomentOfTruth» = dt) = Knowledge. »Confirmed Realization»; — »I have 2 feet».

Earth’s Iron Core — its detailed consequential mathematics — derived from the Planck constant h=mcr neutron equivalent atomic nucleus. with further (Nuclear formations — Basic Carbon Matrices from Concentric Atomic Production);

— All celestial bodies begin from a Dmax neutron mass state (K-cell Heat Physics, K-cell Detonation., K-cell contraction, General Cosmic State Law:

• gravitational redshift (modern academic consensus: ”dark energy”: same math, different statements: Ai machine inquiry confirms) proves the general K-cell universal mathematical physics)

— Light’s gravitational dependency (Application P75) certifies: neutron decay develops fastest in the Celestial Body spherical center where the g-potential i lowest, analogously c-divergence is the greatest.

— Celestial body surface neutrons decays last: hydrogen plus underlying layers of Oxygen16 secures WATER on the body surface, all without exception.

— Different body masses then certifies (internal detonating physics from the initial central neutron decay) the differentiation between planets and stars (lowest 6 Jupiter masses), stone or rock bodies and gas bodies.

End of Short — related physics and mathematics — Cosmological Introduction.

CWONsynth ¦ Recognition ¦ Alt3 ¦ AP75 ¦ RelPM ¦

TeClaNeaR: Aug2026 — SummingJul2023 ¦ INTROrZ ¦ rZ2023 ¦ rZ2023ER ¦ BehindTNED ¦ rZiteration ¦ DiffRunits ¦ Result ¦

TNED CLARIFYING NUCLEAR RESOLUTION

A short description of the 2023 UH presentation in

TNED EXPLAINS ATOMIC NUCLEAR EXPERIMENTAL PHYSICS

The Atomic Nucleus — general survey Jul2023

SummingJul2023: TeClaNeaR

Summing The Jul2023 presentation

By formulating a Fake TNED toroid equation (rZ[SCALE (1)])

for testing on experimentally collected (Blue: Angeli2004) "nuclear RMS charge radii" data

(»first rZ approximation», 2003)

its regular TNED form (rZ)²/r gave close cohering results with the Angeli collected data.

The "Faked" TNED part consist of a (regular) variable iterative toroid (tCON) volume constant (0.0033095408, nominal 0.0033 T25 Coulomb). Its purposes is only added to investigate/examine a match with the experimental data. And as such (rZ2023) it vindicated a closest TNED match: no definite proof. But clear coherent TNED provision:

• the experimental subject is not a sphere, but a Planck constant fractal toroid: TNED.

That short summation would be the whole explaining story behind the 2023 UH presentation

TNED EXPLAINS ATOMIC NUCLEAR EXPERIMENTAL PHYSICS.

The actual content exposes the developing details — along with some reckoning errors.

(The toroid terms in the 2023 edition is rather demanding. A certain refinement NucDed is given in this presentation, along with a separate Part 2 in Revisiting Hofstadter 1956+).

— The end picture (Orange: rZ2023) came with two equations (1) and (2) below in rZANA.

INTROrZ: SummingJul2023

N3m15

THE rZ ANALYSIS 24Aug2026 — nuclear charge — Ze — details

The original rZ terminology

.. emanated here in UH from the 2023 TNED examination of the pioneering Hofstadter electron scattering experiments 1956+ ..

.. toroid nuclear charge radius extension from central toro well ..

As stated in ExplainNUCLEARrZ (2025):

— TNED CONCEPT of rZ had no representation in TNED from the start (TNEDbegin1993).

• rZ (first from 2023 in Revisiting Hofstadter Part 1) here in TNED has come to denote the flat radius extension from the TNED deduced Planck constant toroid central well vertical axis (J0) to the nuclear gravity circle radius (r = rG).

— The ReHofPart1 aimed at examining the relation between rG and the, eventual, Hofstadter data suggested possible rG-deviation then termed »rZ»: the toroid charge (atomic number Z) extension from toroid center.

— As it turned out; the rZ Hofstadter examination paved a way for comparing the total (Angeli2004) world collected nuclear RMS ”charge radii” data on the form

(rZ)²/rG = (rZ)²/(½r₀√A), A mass numbers > 1

It exposed (rZ2023) to have significant coherence with the Angeli2004 data. However still only as a regular »iteration» approaching the collected experimental data (BehindTNED).

— At that point (approaching the UH story 2025, ExplainNUCLEARrZ), direct possible TNED (consequential mathematics) nuclear (spin) details vindicated a possible (for further test) opening, suggesting that

• rG = rZ — in general — offering further closing nuclear theorization.

— As we still are on the investigating level on these details, the rZ now (Aug2026) have the status of »a regular rZ».

— As we still are in search for more hard experimental data proof, and until disclaimed, the term rZ is (here) used analogous to the nuclear gravity circle radius r=rG, as illustrated above.

rZANA: INTROrZ

TNED HAS NO VOLUMETRIC CHARGE DISTRIBUTION.

TNED deduced Nuclear charge is distributed over surface area. Not volume.

1 2 3 4

• C/M³ aspects are then only related to the MAC conventional QCD particle experimentation implications.

• Relative the TNED order, these MAC/QCD results can then be compared to the TNED corresponding parts:

• adapting Z/e-constants connected to TNED nuclear radii.

— That was what the rZ analysis (Jun2023) was all about:

• using the 1956 Hofstadter electron scattering data, searching for TNED connections (1), DEDUCINGrZ,

(1) r_Z(SCALE) = [1/(rG)³ + 0.0033095408 T25 A/Ze]^–1/3/r₀ = rZ/r₀

(2) (rZ)²/rG = (rZ)²/(½r₀√A), A mass numbers > 1

The constant coefficient 0.0033095408 (unit: Coulomb) came from the TNED investigation of the 1956 Hofstadter electron scattering data:

— It has no other meaning here than

»just an Angeli2004 FIT, TNED coefficient» (using OpenOfficeCalc cell code to examine the differences).

rZ2023: rZANA

we found in 2023 that the world collected data (RMS r nuclei) from Angeli2004 satisfied

(approximately from mass number 30 up to the end comparing chart at 83Bi209)

equation (2): Mass numbers from 1-30 were early already explained by detail between TNED/MAC (AngeliTNED):

TNED: THERE IS NO REAL PHYSICAL ”QCD” — ONLY EXPERIMENTAL RESULTS BEING SO WEIGHED IN MAC ..

PROOF:

TNED:s »rZ-QCD nuclear charge radii»:

— »spotting the modern experimental Laser Capability of Viewing the TNED Toroid atomic nucleus ..» ..

• The Weizsäcker water drop model gives huge deviations on the first light nuclei

— while TNED pinpoints these atomic mass values at the extreme of experimental results (See detailed in ComNorm).

— The overall picture points to that the MAC QCD idea is »wrestling» with

• (laser) nuclear (spherical) concepts that needs »correction coefficients»

• to match the modern academic established QCD theory idea of the atomic nucleus.

rZ2023ER: rZ2023

Experimental Resolution

of the 2023 PART 1 Revisiting Hofstadter 1956 pioneering electron scattering experiments

ATOMIC PHYSICS SHOULD BE THE MOST CLEAR TO ANY ALIVE HUMAN. TODAY, ESTABLISHED IDEAS, IT IS THE MOST ABSTRACT CONFUSING SUBJECT OF ALL.

• TNED NUCLEAR RADIUS MATHEMATICS (TNARC)

• have no nuclear charge (Ze) provisions. No way.

• The (rZ)²/r alignment of the Angeli2004 collected world data on nuclear (RMS) radii data

• is the »TNED Corrupted MAC-QCD» Corrected Coefficient VERSION of

• the Angeli2004 collected EXPERIMENTAL RESULTS

• on TNED defined nuclei — TNED says. MEANING:

— The (Anglei2004) collected experimental data suggests that THERE IS an aligned TNED rG-rZ connection

• however Skewed as expressed by equation (1) — altering on the corresponding Angeli2004 data curve (blue);

• The MAC-QCD model blocks TNED — demanding »modeling inputs» — rendering

• »the experimental results»;

— rZ (»says the experimental results») have (says TNED) a clear rG (or IS the)

• connection to a nuclear center extension (rZ) of a nuclear charge

• on the Surface of the top spinning TNED (Planck constant Neutron) defined nuclear toroid.

— In other shorter words:

THE EXPERIMENTAL RESULTS STRONGLY SUGGESTS THAT THE TRUE TNED ATOMIC NUCLEUS

HAS A (rZ) NUCLEAR CHARGE SURFACE EXTENSION FROM THE TOROID CENTER TO MAX rG

• rG, the nuclear gravity circle radius (TNARC), r = rG = ½r0√A, A mass number from A=2, r0 = 1.37 t15 M = rG ¦ A=1:

• We use the 1900s traditional proton gravity circle radius (HANDBOOK OF PHYSICS, McGraw-Hill series)

r0 = 1.37 Fermi = 1.37 t15 M as the basic (neutron) proton A=1 toroid aggregate

— securing our here related physics reference (TNED) to be the unique testing foundation. Even Shorter:

• Experimental results points to a TNED resolution where rZ = rG — for all nuclei,

• for further examination.

BehindTNED: rZ2023ER

TNED REASONING BEHIND

As we know (»TNED+EXPERIMENTAL=TRUE» ¦ ExperimentalConfirmations ¦ NeutronSquareSolutions ¦ ComNorm), the stablished MAC-QCD nuclear theories have least differences on the heaviest nuclei. So if we would select a specific region to test, further, on »TNED+Experimental=True», we would select experimental nucleus in the heavier part of the nuclide chart. In this presentation we continue to focus on the stable nuclides, generally from 1H1 to 83Bi209 (later [recent] research has claimed indications that also the 83Bi209 is unstable, however with a huge half life value).

When MAC-physicists experiment on — says TNED — atomic nuclei (left above) — »light-visual (laser)» optimal nuclear surface covering volume — the experiments cannot (directly) probe the inner (right above) transverse toroid rings — less effective toroid total surface covering volume. Instead the experiments reflect the general top (experimentally viewed spinning as »a sphere»; the toroid form is hidden) spinning (Planck constant) nucleus: »more than true», TNED says:

• the experimental data exposes more volume than true volume (within reasonable probing particle energy levels).

• LIGHT (laser) probing has different (LILYC) capabilities than massive (electron scattering) resources.

— Laser probing on atomic nuclei adds further »halo» nuances (»nuclear shadow measuring»). And so is the atomic nucleus presented today (WikipediaQuote). Namely as something (highly) diffuse. Not at all universes most, all categories, sharp form of gravitation.

In order to approach the experimental results — TNED continues — we TEST to add nuclear volume (on the experimentally specified nuclei), examining (with the simple TNED nuclear equations) »if there is anything in there» worth observing. Did we find any .. ?

— EXAMPLE — the (Blue) Angeli2004 collected world data on nuclear RMS radii (in Fermi = t15 M units):

rZiteration: BehindTNED

rZANA:

OpenOfficeCalc generated from available Data Sources — NuclearSize2023c26.ods — Tabell4 Columns BH¦BL — Graphs BP259 ¦ 24Aug2026

We set up the actual nuclides in a table (OpenOfficeCalc). We insert the TNED calculating math part in its cell and take its entire column values (mark 1:st cell and all the following, whole column, then Ctrl+D). We input a variable (tCON) as the actual 0.0033 .. value. Changing its value, the orange curve receives different end positions. The tCON value of 0.033 is the optional fit to the Angeli2004 data curve.

— We care little about the first light nuclei (blue) overshooting part — as we already know that MAC-theory (interpretations, type Weizsäcker equations) have very poor connection to experimentally measured atomic masses.

— The interesting, and challenging, part begins from around mass number 60 (the heavy part of the nuclear chart). The differences decrease as the end nuclide 83Bi209 is approached.

DiffRunits: rZiteration

The different radii units:

In MAC-QCD and (laser) experimental particle physics the term and concept of a ”nuclear radius” (WikipediaQuote) have no way similar meaning to TNED related physics and mathematics. Exactly what the MAC ”Nuclear rms charge radii” preference in the collected Angeli2004 data means, Units in 1 Fermi = 1 t15 M is — really — unclear. The MAC term ”RMS” (Root Mean Square) is (as presented on the web) a highly abstract (experimental) statistical term. It has (absolutely) no simple or direct geometric meaning or significance.

Connecting the TNED testing transverse ring toroid volumes

HOWEVER, given the partly close connected results .. it is apparent that the TNED suggested rZ parameter HAS experimental connection.

(3) r_Z(SCALE) = [1/r³ + 3ΨkA/Ze]^–1/3/r₀ = rZ/r₀

The whole TNED testing idea is based on the k-factor (given in a Coulomb unit). As the 3Psi factor (3Ψ) defines the three transverse toroid ring volumes, any k-value larger than exactly zero (0) will introduce a (fictitious experimental matching) rZ-function different from r=rG.

— The triple ΨkA then enlarges each transverse toroid ring volume, approaching (testing) the experimental features (always probing the top spinning nucleus, which hides a larger volume than the transverse rings).

— In the Jul2023 evaluations, the first (approximated) and used k-number was k = 0.001855. With the adopted tCON = 0.0033095408 (calculating among the approximations), the corresponding enlarged transverse Ψ volume coefficient became 0.5947063465.

Using these initial 3Ψk = 3 · 0.5947063465 · (k=0.001855) = tCON = 0.0033095408, we see that— really —

(4) tCON/3 = Ψ · k

Result: DiffRunits

Result:

Still increasing the transverse toroid ring volume value (Ψ) only narrows the k-value — presenting exactly the same end form result (rZiteration). So the end picture reveals »parametric ditches» — pointing to (MAC-QCD) »computer modeling». However, that »story» entails unknown details here. The point is though given:

»strong suggested experimental proof for that the TNED toroid nuclear charge surface covering does not extend the central distance of the nuclear gravity circle radius».

— The Highly Enthusiastic QCD experimentalists (not at all aware of the atomic nucleus as a spinning hollow toroid) never had a clue of that one. It is all in TNED.

But we would need »further strong suggested proof» to strengthen that (our. here) first indicated TNED »experimental suggestion» status.

Continue on

Revisiting Hofstadter 1956+ Part 2.

Using another method for investigating Nuclear Volume — behind Nuclear Surface:

determining nuclear charge distribution from electron scattering

TeClaNeaR ¦ SummingJul2023 ¦ INTROrZ ¦ rZ2023 ¦ rZ2023ER ¦ BehindTNED ¦ rZiteration ¦ DiffRunits ¦ Result ¦

ErrorCheck: Aug2026

Checking errors on the previous 2023 edition ....

Checking errors on the previous 2023 edition ....

N3m15

THE rZ ANALYSIS 24Aug2026

error 2023:

The 2b(πa)² form is correct for the transverse toroid ring volume (Ψ).

But the expression (π/4)²(1 – 7/2 + 2√3) is corrupted:;

Correct form for b should be (2023 designations)

b = R – a (R=1). Not

b = R – i (i = 7/2 – 2√3)

Aug2026:

The correct connection with present revised and refined terms is:

The correct Ψ formula expression — Aug2026 refined (checked, rechecked) terminology:

Aug2026, this present edition (CHECKING ON NucleusDeduction):

---------------------

riV/3 = 2pi(d/2+r) · pi(r)² ; Ψ the rG=1 TranverseToroRingVol

= 2(pi)²(d/2+r) · (r)² ; Mod1; A > 1 ;

r = rG/(2.2320508) ; rG = ½r0√A ; r0=1; rG = ½r√A

d/2 = rG – (2r + R) ;

rG/R = 14.4282032303 ;

d/2 = rG – (2r + rG/14.4282032303)

d/2+r = rG – (2r + rG/14.4282032303) + rG/(2.2320508)

= rG – 2r – rG/14.4282032303 + rG/(2.2320508)

= rG – 2r

= rG – 2rG/(2.2320508)

= rG(1 – 2/2.2320508)

rG = 1; A > 1 ;

riV/3 = 2pi(d/2+r) · pi(r)² ; Ψ the rG=1 TranverseToroRingVol

= 2pi[rG(1 – 2/2.2320508)] · pi[rG/(2.2320508)]²

= (rG)³ × 2(pi)² × (1 – 2/2.2320508) · [1/(2.2320508)]² ; CHECKED

= (rG)³ × 0.411908351 ; Checked

----------

quite different from the 2023 result:

----------

= 0.5947063465 ;

AS IT TURNED OUT

— NO BIG DEAL: IT IS ALL ABOUT A COEFFICIENT VALUE ANYWAY:

Aftermath:

The 2023 (Psi, Ψ) error is — still — irrelevant:

The net end picture can use alternative Ψ values along with the (iterative) constant (tCON = 0.0033) in

(1) r_Z(SCALE) = [1/(rG)³ + 0.0033095408 T25 A/Ze]^–1/3/r₀ = rZ/r₀

on the (tCON = 0.0033) form

(4) tCON/3 = Ψ · k ; original 2023:

k = 0.001855 ¦ T25 ; the Hofstadter TNED difference

The end result is independent of Ψ k,

so our designation and math error in the 2023 edition makes nothing to the actual 2023 The Final rZ end results: see rZ2023. Same end.

ErrorCheck ¦

NeutronBegin: Aug2026— NeutronDetails ¦ ConAtomic ¦ AiLIE ¦ CompiledNuclear ¦ EXcon ¦ KrischCollected ¦ Wanted ¦ NucPro ¦ NucTNED ¦ KingsTWO ¦

ExplainModulus

Planck constant — Nuclear spin — NucleusDeduction Dec2025

DETAILED ATOMIC AND NUCLEAR PHYSICS IN TNED

— related physics and mathematics (Aug2026)

NeutronDetails:NeutronBegin

Beginning from The NEUTRON — in TNED only: the equivalent Planck constant (never so mentioned in MAC)

The Planck constant h=mcr

h 6.62559 T34 JS = 1.0086652u · 2.99792458 T8 M/S · 1.3196610608 t15 M = Planck’s constant = m c r = h :

u 1.66033 t27 KG = mC12/12; 1 Dalton — its numeric FORM often named ATOMIC WEIGHT [ U; m = NUu; N = m/Uu — not used in MAC; see The MOL concept ]

m 1.0086652u, neutron mass mn ¦ me, electron mass 0.000548598u

c 2.99792458 T8 M/S Light’s divergence in free space — [ neutron ] nuclear spin associated property

r h/mc = 1.3196610608 t15 M: NEUTRON GRAVITY CIRCLE SPIN RADIUS: 1.32 Fermi

mn/me = 1.0086652/0.000548598 = 1838.6235458387 = 1818 + 18 + 2.6235458387 electron masses (±e);

Planck constant — never mentioned as The Neutron Equivalent in modern academic corridors

h = mcr = neutron mass · light’s divergence in free space — neutron gravity circle radius

We associate c as the fundamental (default) value connected to the neutron’s rotational SPIN velocity property.

ConAtomic: NeutronDetails

Conditions as related (and observed):

The atom sums zero spin ±s and zero charge ±e: = zero magnetism: no electric or magnetic inner net forces:

— The atom i forced to sum a net zero on force and moments (inner/outer exchange electro-mechanics only):

— The atom needs no refill to continue to work: no inner electric resistance or mechanic inertia or inductance; zero moments. zero forces;

— Only remaining after (Pair Annihilation) zero sum force and moments is:

• mass (m), so it can be transferred to massless Planck energy heat and light: E = hf = mc²: star physics — just prepared for mass destruction (SunLight);

Atomkärnans elektromagnetiska mekaniska vektoriella egenskaper kan inte beskrivas eller härledas utom på N3 toroidens Plancks konstant (h) — neutronens — villkor: atomkärnan är INTE någon sfärisk partikel. Atomkärnan har inga interna snurrande kulformer (QCD, Citatsamling, experimentella bekräftelser redan 1979-87). Helheten förklarar — allt.

———————————————

NuclearDeduction ¦ NucTNED — all electromagnetics collected¦ FEC — collection enhanced

The reader is strongly advised and recommended to try, with all the power available in our universe, to Disclaim the above illustrated vector orders compiled. Why is that? There is only one general universal profitable solution to that type of engagement: Enhanced knowledge. Why is that? Only two possible outcomes exist. Either the statements are shown to be valid — or not at all. Either way, knowledge wins.

— The (h) neutron-proton inner transverse three J/3 rings are never seen in real physics as such illustrated. They are hidden by the nuclear top spin feature, the right illustrated part. However (Quote below in EXcon) sufficiently high particle energy (polarized proton collisions, 1979-1987) collisions between protons have certified significant results — contradicting general modern academic QCD ideas of the nature of the atomic nucleus.

The experiments have since »been quieted down». Scanning Internet on the subject: practically nothing of the actual Krisch’s own quoted below aspects are seen. It has all been »watered out» in stating and claiming the results to be »important contributions to the quark theory» (spinning spherical balls inside nuclei). Nothing left of the original Krisch QCD critics:

” The experiments even call into question the currently accepted model of the proton's internal structure, which holds that a proton consists of three smaller constituents known as quarks, held together by the strong nuclear force (the force described by QCD).”, as Quoted from SA Aug1987 below.

Shorter: The Man was ignored. Come again.

AiLIE: ConAtomic

An Ai (GPT-5.nano 26Aug23026) claims: ”.. The Krisch experiments .. Electron scattering High-energy electrons were directed at protons ..”. Nothing of the kind exists in the Krisch experiments 1979, 1987. This author have both the SA issues May1979 and Aug1987: All Ai lie. That is a serious proof of (that this Ai GPT-5.nano machine is) a definite no go. Be careful — use it to prove its inappropriate statements (It crashes on SERIOUS descriptions). If original sources cannot be quoted, statements ABOUT the sources content are »academic gossip».

Alan Krisch passed 2020 at the age of 81. TNED would never have come about without his and his colleagues work. Thank You.

CompiledNuclear: Aug2026 — AiLIE

Principal structure of mass — Explain Mod0 Mod1

———————————————

NuclearSPIN ¦ Revisiting Part 2 of the Hofstadter pioneering electron scattering experiments 1950s ¦ TNED Nuclear Deduction ¦

The Derivation ¦ Deducing Nuclear Radius ¦

EXcon: CompiledNuclear

Experimental Confirmations [ACADEMY REJECTED — never mentioned since .. questioning the entire MAC consented quark idea (QCD)]:

”Most high-energy physicists were quite sure that spin would be unimportant in elementary-particle collisions at billions of electron volts of energy. For years this belief was tested only in a series of difficult experiments done by Owen Chamberlain and Emilio Segré of the University of California at Berkeley, among others. Then in the late 1950's Anatole Abragam of the College de France and Carson D. Jeffries of Berkeley suggested building polarized proton targets. The technique, which has been quite successful, relies on a low temperature and a strong magnetic field to polarize the spins of certain electrons in frozen beads of target material; the magnetic field causes the spins of the electrons to ”line up.” Microwave radiation is then applied to transfer the spin alignment of the electrons to nearby protons, making them spin in one direction. Experiments employing polarized proton targets in the 1960's and early 1970's at Berkeley, CERN (the European laboratory for particle physics) and Argonne revealed small but interesting spin effects in high-energy collisions. Nevertheless, most high-energy physicists still believed spin was not very important and would become even less so at higher energies.

In 1973 my research group inaugurated a different approach at the Zero Gradient Synchrotron: we polarized the beam as well as the target.”.

SCIENTIFIC AMERICAN August 1987 Collisions between Spinning Protons p32col.2b

”it has turned out to be quite wrong”

SCIENTIFIC AMERICAN May 1979 The Spin of the Proton p58col.1m:

It has long been thought, however, that the influence of spin should decline as the energy of the collision increases. The reasoning behind this assumption is simple: the energy associated with a proton’s spin is constant and so it becomes an ever smaller fraction of the total energy as the collision becomes more violent. At a sufficiently high collision energy it should make no difference whether two colliding protons are spinning the same way or in opposite directions.

Only in the past few years have experimental techniques been devised for testing this assumption. It has turned out to be quite wrong.

”fact is that the spin directions do make a big difference”

SCIENTIFIC AMERICAN August 1987 Collisions between Spinning Protons p32col.2m:

The energy associated with the spin of a proton is constant, and so the role played by spin should diminish as the energy of the collision increases. At sufficiently high energies it should make little difference whether two colliding protons are spinning in the same direction or in opposite directions. The fact that the spin directions do make a big difference suggests that our understanding of how protons interact with one another is incomplete. The experiments even call into question the currently accepted model of the proton's internal structure, which holds that a proton consists of three smaller constituents known as quarks, held together by the strong nuclear force (the force described by QCD).

(Established ideas of natural physics [MAC]: The conditions were better year 1311: Retarded. Low educated. Intellectually disabled. Perfect Natural Intelligence: Too Low Input).

(The Krisch group experiments fully vindicate [and support] related physics and mathematics: the atomic nucleus is NOT a sphere with inside rotating balls).

KrischCollected: EXcon

The Alan D. Krisch Scientific American collected quotes in UH:

———————————————

The Krisch Group Results from SA 1979 ¦ Experimental Confirmations ¦ TNED illustrated Krisch quotes — Collected Quotes

The provoking Krisch group results here in UH specifically TNED illustrated:

COLLISIONS BETWEEN SPINNING PROTONS

Ursäkta::

Utför modernt akademiskt samtycke medvetet undanhållande av experimentella resultat som uttryckligen innehåller utsagor som ifrågasätter etablerade synsätt och föreställningar, speciellt på området kärnfysik? Det ser (tammetusan) så ut.

(Alan Krisch:s EGNA meningar, så framställda i SA artiklarna 1979-87: inte ett spår funnet @Internet. Jämför AiLIE Ai maskinens direkt bevisbart förljugna sammanfattning i citat).

(Tillståndet nu Aug2026 är definitivt värre än år 1311).

”opposite spins seem to pass through each other”

SCIENTIFIC AMERICAN May 1979 The Spin of the Proton p58col.1mb:

Protons with opposite spins often seem to pass through each other without interacting at all.

TNED ILLUSTRATED AND CONFIRMED FUNCTION OF THE KRISCH GROUP EXPERIMENTS ON COLLIDING PROTONS — Scientific American May1979 and Aug1987

”objects in the proton spinning very rapidly”

SCIENTIFIC AMERICAN May 1979 The Spin of the Proton p58t:

When two protons collide, the outcome depends on which way the particles are spinning. The effect seen in violent collisions suggests there are objects in the proton that spin very rapidly

”protons spinning in the same direction rebound”

SCIENTIFIC AMERICAN May 1979 The Spin of the Proton p58col.1mb:

A recent series of experiments has shown that protons spinning in the same direction are much more likely to rebound violently than protons spinning in opposite directions.

”antiparallel spins seem to pass straight through each other”

SCIENTIFIC AMERICAN May 1979 The Spin of the Proton p69t.ill:

when the spins are antiparallel, the objects seem to pass straight through each other

”opposite spins often pass through each other as if transparent”

SCIENTIFIC AMERICAN May 1979 The Spin of the Proton p70col.2b:

When two protons spinning in the same direction collide head on, they almost always scatter violently. When the same particles are spinning in opposite directions, they often pass through each other as if they were transparent.

”a surprising dependence on the direction of spin”

SCIENTIFIC AMERICAN August 1987 Collisions between Spinning Protons p32t:

The outcome of a collision between two protons shows a surprising dependence on their directions of spin. The results challenge the prevailing theory that describes the proton’s structure and forces

Wanted: KrischCollected

Be aware of Ai reports not quoting actual sources

The Krisch group experiments clearly, as quoted (EXcon), questions the established ideas (QCD) on several points. But the central Krisch group result aspect, the Questioning part, and the experimental LIGHT behind, seems to have been completely lost in present (Aug2026) academic archives. Besides that:

To receive polarized proton spins, its electrons were utilized with a strong magnet (photo in the SA issue May1979). Besides that: no further electron use.

The exemplified Ai machine GPT-5.nano (GOOGLE, DuckGo) claims the Krisch experiments was all about ”electron scattering”.

— Nothing such exists in the Alan Krisch SA publications May1979 (The Spin of the Proton) and Aug1987 (Collisions between spinning Protons. This author has both SA Scientific American issues May1979 and Aug1987. Absolutely clear).

— It is shameful to fob linguistically well speaking fuckups onto humanity, serving the public with produced lies, as if a gala of global charity on not seriously checked sources. Provably not caring about checking its sources, generating novels on invented content and context, is termed fraud — executed by a conjurer’s juggling fiddling wangle. Come again. Say again.

Svenska, kort: taskspeleri.

NucPro: Wanted

Basic TNED related physics and mathematics only

ATOMIC NUCLEAR PROPERTIES, PROVISIONS AND CONDITIONS — in 9 points:

As observed:

• 1. loss free:

— needs no refill to continue to work;

• 2. no inner rotational inertia (Compare experimental macroscopic GyroPhysics):

— inertial moment = 0; electric resistance = 0; electric inductance = 0; current property: constant (c-related: h=mcr);

— sum of all forces and moments = 0; charge ±q, spin ±s; remaining mass can be transferred to Planck (”spin”) energy E=hf; star physics;

Explain:

(Macroscopic) Rotational Inertial Momentum (Ĵ = mr²) means (mr²) mass over rotational disc extension (volume) area:

— Meaning:

• 2.1 no inner inertial property: The atomic nucleus is free from mass over disk:

• 2.2 no inner mass volume: MEANING:

— Nuclear mass refers only to a

• 2.3 gravity circle radius (Angular momentum = Inertial momentum = constant — changes only by fusion-fission):

• 3. m = (n→∞) · m/(n→∞) — resembling a

• 3.1 constantly perpetually dynamic division of every specific ring mass part into smaller ring mass parts (h-rings)

— fractals of diminishing top spinning toroid rings with transverse sub-levels of smaller rings (only possible fractal morphological solution);

— forming a infinitesimally THIN nuclear mass-shell which inside mass g-potential approaches infinity;

— center of gravity is the toroid gravity circle radius center.

• 3.2 Just by plain mathematical consequences (QI math),

— on already well relatable basic physics and mathematics:

• 3.3 No speculation. No theory. No consensus.

NucTNED: NucPro

Spinning electric coil, hollow toroid, in TNED (related physics and mathematics)

— summing atomic and nuclear provisions (as observed) in spin (Application P65), electric and magnetic features

The only possible way of understanding the inner organization

of the electro-magnetic-mechanics of the atomic nucleus: mass, charge, spin.

Inner losses = 0 — the different spins do not interfere or destroy the function. What we know:

No spherical morphology can explain the above addressed electromagnetic-mechanical cooperative connections. If any provable disapproval found: please do share.

— Why couldn’t MAC have proposed this »simple toroid [QI math]» solution .. (from around 1932: Chadwick discovers the neutron) .. ?

— Rephrase: is there any [elementary] detail at all that MAC did NOT miss .. ? ..

— Is that an accusation .. ?

— Yes, absolutely — only if it is appropriate, which it is not, to accuse someone for being ignorant. That would indeed be the practically most galactic stupid.

KingsTWO: NucTNED

Related Atom- and Nuclear physics two Impulse (e.g. angular momentum) and Force equations:

J(0K) + 3J(1K) = 0 balancing top (magnetic BK) and transverse (magnetic BT) — only way to secure the proper electron-nucleus electromechanics

F(BT) + F(eZ) = 0 general chemical electron sharing connection — all connected (summing molecular) atoms share the same electron mass

Experimental observations 1956¦7, see WuREF ¦ Wu1957 — detailed ¦ IllustratedTNED: The atomic nucleus emits electrons ”preferentially” opposed the nuclear spin vector direction, confluent with that for positrons.

THE ATOMIC NUCEUS: A

• 4. hollow toroid (Planck fractal) RING with sub-levels of transverse fractal RINGS;

• 5. A final principle, Principal

• 5.1 limitless thin nuclear shell where its

• 5.2 gravity potential (a) approaches infinity (N3View):

• 5.3 the fundamental form of gravitation

• 5.4 the atomic nucleus (the neutron, building heavier nuclei-atoms), its gravitational potential (a)

a · (n→∞) = (n→∞)Gm/r² = G · [m/(n→∞)]/[r/(n→∞)]² = G · (n→∞)(m/r²) ¦ PlanckRING2 ¦ (n→∞)²/(n→∞) = (n→∞); MEANING:

• 6. THE ATOMIC NUCLEUS cannot be compressed: it is already standing on zero.

• 7. THE ATOMIC NUCLEUS has no volumetric mass morphological connection.

• 8. THE ATOMIC NUCLEUS has Magnetism and Electric Charge (±q by spin ±s);

• 9. THE ATOMIC NUCLEUS regulates its atomic electron mass (EC [ElectronCapture], ±e emissions; NeutronDetails);

(Deducing THE PERIODIC SYSTEM OF THE ELEMENTS from Kepler Resonances and The Nuclear Matrix Algorithm ¦ NuclearAtomAlgorithm).

NeutronBegin ¦ NetronDetails ¦ ConAtomic ¦ AiLIE ¦ CompiledNuclear ¦ EXcon ¦ KrischCollected ¦ Wanted ¦ NucPro ¦ NucTNED ¦ KingsTWO ¦

NucDed: Aug2026 — Corrections ¦ CompiledToroidFormulae ¦ AppliedToroMath ¦ TopVdivTrans ¦ Sources ¦

FURTHER COMPILED EDITIONS ON DEDUCING THE ATOMIC NUCLEUS

Detailing

THE TNED ATOMIC NUCLEUS — its fundamental deduction

Related physics and mathematics Aug2026

Corrections: NucDed

CORRECTIONS 9Aug2026 from previous faulty prints:

CAT2025D.htm#AreaANDvolume

Basic geometry

PREPARING FOR EXPERIMENTAL COMPARISON

Securing and checking the terminology and its expressive accuracy

Previously (several) error mishaps (transfer errors) have urged this review

(»No big deal» — we were just warming up ..)

(This is supposed to be The Real Steel version ..).

INITIAL ORIGINAL SCHEMATICS, (refined, simplified) designations:

CompiledToroidFormulae: Corrections

AppliedToroMath ¦ ErrorCheck ¦ ToroSpinVolAR ¦ FormulaeTEST ¦

From ToroNuclearBasics 2025

N=3:

K = 2/√3 – 1 = 0.154700538 = R/r ¦ 1/K = 6.4641016151

r = R/K

CHECKING ON THE CORRECT MATHEMATICS:

CAT2025D.htm#AreaANDvolume

THE TOP SPINNING TOROID FORM: error (see z):

Top spin toroid surface = A = 2π(D/2+R) · 2π(d/2) THE OUTER TOTAL VISUAL TOROID FORM

= 2π(R + 2r + d/2) · 2π(2rz/2) ?????? .. d = 2rz ??? (.. tired .. excited .. ? .. come again ..)

= 2π(rK + 2r + 2rz/2K) · 2πrz

= 2πr(K + 2 + z/K) · 2πrz

= (2π)² · r²z(K + z/K + 2) ; z = m – 1

[No other errors [ed. Dec2025] — as checked, Aug2026].

corrected 30Aug2026

CHECKING ON THE CORRECT MATHEMATICS:

CAT2025D.htm#AreaANDvolume

THE TOP SPINNING TOROID FORM: corrected

Top spin toroid surface = A = 2π(D/2+R) · 2π(D/2) THE OUTER TOTAL VISUAL TOROID SURFACE FORM

= 2π(R + 2r + d/2) · 2π(2r + d/2)

= (2π)²(R + 2r + d/2) · (2r + d/2)

= (2π)²(rK + 2r + 2rz/2) · (2r + 2rz/2)

= (2π)²(2r)²(K/2 + 1 + z/2) · (1 + z/2) ¦ ½(2 + z = 1 + m) = ½(m +1)

= (4π)² · r²(K/2 + 1 + z/2) · (1 + z/2) ; z = m – 1

m¦m0 = Mod0 = 7(1/√3 + 1/2) + 2√(7 + 12/√3) = 15.00555349946510000000; A=1

m¦m1 = Mod1 = 1/2 + 1/√3 = 1.077350269 ; A>1

---------------------------------------

r = d/2z; rz = d/2

= R/K .. (CHECKED)

z = d/2r (MODULUS) — inner ring Ø (large) divided with ring body Ø (small)

d/2r = z

d/2 = zr ;

rG = R + 2r + d/2 ;

d/2 = rG – (R + 2r) ;

d/2r = [rG – (R + 2r)]/r ;

= z

---------------------------------------

N=3:

NSpin2025copy26.ods — Tabell1 W16

NuclearSize2023c26.ods — Tabell1 J39

TEST with (rG=1 ¦ A=1); A (N=3, K = 2/√3 – 1 = 0.154700538);

A = 2:

rG = 1/√2

= 0.7071067..

(rG/r) = 2.2320508

r = 0.3167969021 = rG/[(rG/r=2.2320508)]

(rG/R) = 14.4282032303

R = 0.0490086513 = rG/[(rG/R=14.4282032303)]

z = d/2r

= [rG – (R + 2r)]/r

= 0.0773502692 — independent of A>1: we can plot in any integer A>1, and the m = z + 1 stays put.

m(A>1) = 1.0773502692 = z + 1 ; as deduced.

---------

Using the same schedule for A=1, also its deduced m = z + 1 is confirmed as checked above.

---------

NSpin2025copy26.ods — Tabell1 W16

NuclearSize2023c26.ods — Tabell1 J39

Top spin toroid volume = A = 2π(D/2+R) · 2π(D/2)² THE OUTER TOTAL VISUAL TOROID SURFACE VOLUME

AppliedToroMath: CompiledToroidFormulae

rG = R + 2r + d/2 ;

= R + D/2 ;

D/2 = 2r + d/2 ;

d/2 = rG – (R + 2r) ; R = rK ; r = R/K

-----------

d/2 = rG – (rK + 2r) ; NuclearSize2023c26.ods — Tabell1 T45 : Numerically Checked on 83Bi209

-----------

r = R/K ;

d/2 = rG – (R + 2R/K) ;

= rG – R(1 + 2/K) ;

d/2 = rG – (R + 2r) ;

d/2 = rG – (rK + 2r) ;

D/2 = 2r + d/2 ;

= 2r + rG – (rK + 2r)

= 2r + rG – rK – 2r

= rG – rK ;

D/2 = rG – R ; CHECKED

---------------------------------------

D = 2(rG – R)

D/rG = 2(1 – R/rG) ; A > 1: NuclearSize2023c26.ods — Tabell1 L41

= 2(1 – 0.0693086994)

= 1.8613826013

---------------------------------------

d/2 = D/2 – 2r ;

D/2 + R = rG ;

tVOL = 2pi(D/2+R) · pi(D/2)²;

tVOL = 2pi(rG) · pi(rG – R)² ;

= 2(pi)²(rG) · (rG – R)² ;

R(A>1) = rG/(14.4282032303)

-----------

t(V/S) = [2pi(D/2+R) · pi(D/2)²]/[2pi(D/2+R) · 2pi(D/2)]

= [pi(D/2)²]/[2pi(D/2)]

= [(D/2)²]/[2(D/2)]

= (D/2)/2

= (D/4)

-----------

TopVdivTrans: AppliedToroMath

-----------

TopVolume div TransverseVolume:

A>1:

————————————————

toV/riV

————————————————

riV ¦ 1/3; EX: A > 1:

riV/3 = 2pi(d/2+r) · pi(r)² ;

-----------

TOP TORO VOLUME is 2.9801996411 times larger than the 3 transverse riV ring volume

toV = 2pi(D/2+R) · pi(D/2)²;

-----------

toV/3riV = [2pi(D/2+R) · pi(D/2)²]/3[2pi(d/2+r) · pi(r)²]

= [(D/2+R) · (D/2)²]/3[(d/2+r) · (r)²]

---------------------

riV/3 = 2pi(d/2+r) · pi(r)² ; ; NuclearSize2023c26.ods — Tabell1 Y49: :

= 2(pi)²(d/2+r) · r² ; ; NUMERICALLY CHECKED on 83Bi209:

= 2(pi)²r(d/2r+1) · r² ;

= 2(pi)²(d/2r+1) · r³ ; ; NuclearSize2023c26.ods — Tabell1 Y50

---------------------

(rG/r) = 2.2320508 ; A > 1: ; c = rG/r [Tabell1 K49, All A > 1]

r = rG/(2.2320508) ;

= rG/c ; ; NUMERICALLY CHECKED:

c = 2.23205080756888 ; NuclearSize2023c26.ods — Tabell1 K49:

---------------------

riV/3 = 2(pi)²(d/2r+1) · r³ ; NuclearSize2023c26.ods — Tabell1 Y50

= 2(pi)²(d/2[rG/c]+1) · (rG/c)³ ; NuclearSize2023c26.ods — Tabell1 P51 Checked : rG/c = r

= 2(pi)²[d/2 + rG/c] · (rG/c)² ; NuclearSize2023c26.ods — Tabell1 Y45 Checked

= 2(pi)²[rG – (rK + 2r) + rG/c] · (rG/c)² ; Checked Y44

= 2(pi)²[rG – (K · rG/c + 2rG/c) + rG/c] · (rG/c)² ;

= 2(pi)²[rG – K · rG/c – 2rG/c + rG/c] · (rG/c)² ;

= 2(pi)²[rG – K · rG/c – rG/c] · (rG/c)² ; Checked Y43

=

2(pi)²rG[1 – K · 1/c – 1/c] · (rG/c)² ; Checked Y51

=

2(pi)²rG[1 – K/c – 1/c] · rG²/c² ;

2(pi)² [1 – K/c – 1/c] · rG³/c² ; ;

=

2(pi)² [1 – K/c – 1/c]/c² · rG³ ; ; Checked Y53

= 2(pi)²[1 – (K + 1)/c]/c² · rG³ ; ; Checked Y54

CHECKED VERIFIED [(83 Bi 209]): NSpin2025copy26.ods — Tabell1 AL27 ¦ 10Aug2026 NuclearSize2023c26.ods — Tabell1 as above

K = 2/√3 – 1 = 0.154700538 = R/r ¦ 1/K = 6.4641016151

r = R/K

c1 = [1 – (K + 1)/c]/c²

= 0.09688235704593 ;

c2 = 2(pi)²c1

= 1.91238107497689 ;

————————————————

riV ¦ A > 1:

riV/3 = rG³ · c2 ; transverse single ring toroid volume

riV = 3c2(rG³) ; transverse all 3 toroid volume (2.9801996411 less than toroid top spin Vol)

= 3(½ r0 √A)(1.91238107497689) ; A>1, mass number

= (5.7371432249)(½ r0 √A) ;

rG = ½ r0 √A ; A>1 nuclear gravity circle radius,

r0 = 1.36646123923569 t15 M ; See ProtonRadius from the (UH original 2003) Neutron Square

= 1.37 Fermi rounded ; »classic HOP values» 1900s science text book value

---------------------

K = 2/√3 – 1 = 0.154700538 = R/r ¦ 1/K = 6.4641016151

NUTGOMAD:

s = 2π(D/2)/2 = π(D/2) ¦ A = ½ π(D/2)² = πD²/ 8

Halvcirkelns tyngdpunkt

bågen ytan

2r/π ¦ 4r/3π

r = 1 0.63661977 ¦ 0.42441318

Sources: TopVdivTrans

PREFIXxSIN:

CIRKELBÅGENS TYNGDPUNKT för godtyckliga (radianer) vinkelsektorer (aRAD), räknat från cirkelns origo

pG = (2r/a) · cos(a/2)

CIRKELSKIVANS SEKTORYTA:

AR = rs/2 = ar²/2

-----

s/2pir = AR/pir² ; AR = pir² · s/2pir = r · s/2 = r · ar/2 = ar²/2 = A°(pi/180)r²/2 = A°(pi/180)(D/2)²/2= A°(pi/360)(D/2)²

Cirkelytan A = ar²/2;

aRAD = A°(pi/180)

PREFIXxSIN:

Webbsökning 15Aug2026 (också verifierat som ovan):

CIRKELSKIVANS TYNGDPUNKT för godtyckliga (radianer) vinkelsektorer (aRAD), räknat från cirkelns origo

pG = (4r/3pi) · cos(a/2)

NucDed ¦ Corrections ¦ CompiledToroidFormulae ¦ AppliedToroMath ¦ TopVdivTrans ¦ Sources ¦

ComparingExperimental: — ToroSpinVolAR ¦ FormulaeTEST ¦ HOFtoro ¦ TwelvePoints ¦ N3View ¦ PointResult ¦ ToroNeutral ¦ ResultsTable ¦ RevisitHofP2 ¦ HOFTable ¦ HofDiagrams ¦ The2DM ¦ HofEndResult ¦ AKSAcollected ¦

BottomLine ¦

Part 2 of Revisiting Hofstadter electron scattering experiments 1956+

DETAILED NUCLEAR INVESTIGATION —

TNED(1993¦2026)/MAC(1956+)

THEORY TO EXPERIMENTAL — or Experimental to Theory

FURTHER PREPARING ON NUCLEAR MATH FOR EXPERIMENTAL COMPARISON

Testing particle experimental results on

Electric Nuclear Charge distribution

on the related physics TNED morphology

PREFIXxSIN

NUCLEAR PROVISIONS — BY TNED

ToroSpinVolAR: ComparingExperimental

Investigating Spin Toroid Volume By Angle

— Was this what the 1950:s Hofstadter electron scattering experiments were trying to probe .. ?

PREPARING TNED Toroid Nuclear GEOMETRICAL DESIGNATIONS

PREFIXxSIN

Equating to a final expression:

Testing on inside ARC length toroidal (rotational volumes). A°(pi/180) = aRAD.

----------

A = 1 ; A, massnumber ; ToroMODULUS = 15.0055535

R = rG/(104.4615242271) ; rG/rG0R

----------

A > 1 ; A, massnumber ; ToroMODULUS = 1.077350269

R = rG/(14.4282032303) ; rG/rG1R

----------

All cases:, A massnumber:

rG = ½r0√A ; r0 = 1.37 T15 M (ProtonGravityCircleRadius) ¦ unit 1;

D/2 = rG – R ;

= rG – rG/M ; A > 1 ¦ M = rG0R ¦ rG1R

= rG(1 – 1/M) ;

-------------------------------------------------

b = (D/2)(1 – sin[A°/2]) ;

rZ = R + b ;

= R + (D/2)(1 – sin[A°/2]) ; D/2 = rG – R = rG(1 – 1/M); R = rG/M ;

-------------------------------------------------

rZ = rG/M + rG(1 – 1/M)(1 – sin[A°/2])

= rG[1/M + (1 – 1/M)(1 – sin[A°/2])]

= (½r0√A)[1/M + (1 – 1/M)(1 – sin[A°/2])]

-------------------------------------------------

rZ/rG = 1/M + (1 – 1/M)(1 – sin[A°/2])

-------------------------------------------------

b/(D/2) = 1 – sin(A°/2) → beginning horizontally from left circle part with A°= 0, - - - →,

approaching the whole diameter length D at A°=360 in PREFIXxSIN.

FormulaeTEST: ToroSpinVolAR

TNED. 17Aug2026

METHOD:

— AS WE ALREADY KNOW BY PRECISION the atomic nuclear gravity radius (rG) extensions, and have the exact TNED description of The Atomic Nucleus, we can test these premises on the actual Hofstadter (1956) reported results, to see »if there is anything concurring in there».

GR =

rG – (pG fromDiscOrigo)

TOP ToroidSPIN VOLUME: WHOLE D-DISC GuldinRotationalRadius ToroORIGO to discAREA pG = DiscGravityPoint

aRAD = A°(pi/180) (D/2 + R) pi(D/2)² 0

————————————————————— —————————————————— ———————— —————

TOP ToroidSPIN VOLUME: WHOLE D-DISC: 2pi(D/2 + R) × pi(D/2)² 0

-------------------------------------------------------------------------------------------------------

:

Top ToroidSPIN VOLUME: Any D-disk PART: GR PREFIXxSIN discAREA pG

——————————————————————————————————————————————————

Top ToroidSPIN VOLUME: Any D-disk PART: rG – [2D/3pi]cos[a/2] A°(pi/360)(D/2)² [2D/3pi]cos[a/2]

————————————————————— —————————————————— ———————— —————

Top ToroidSPIN VOLUME: Any D-disk PART: 2pi(rG – [2D/3pi]cos[a/2]) × A°(pi/360)(D/2)²

-------------------------------------------------------------------------------------------------------

A°(pi/360)(D/2)² = a(D/2)²/2, = a(D)²/8

HOFtoro: FormulaeTEST

We determine, for Test, the following general Equative Testing Expression:

HOF/HOF = 1 = Toro = True — if, and only if, the Hofstadter experiments align Directly with our deduced Planck ring constant h=mcr=6.62559 t34 JS Neutron atomic nucleus.

EXPLAIN:

• Namely: IF HOF/Toro = HOF, then the statement is fully verified;

• OTHER: IF HOF/Toro = Hof, we WEIGH that deviating HOF Hof-value AS CLOSE AS POSSIBLE TO the Real HOF-value in Column H below,

(HOF/Hof = Toro, Column G below in the ResultsTable)

in examining Hof at what Angular Degree (the HOF-table) That Real HOF vale points at,

• with a further examination:

— If that result makes any sense at all WITH our precision given Toro mathematics and Planck constant angular physics, the HOF experimental results will also make sense to the Toro mathematics and physics. Or else: — not at all.

— Why not test the HOF C/M³ directly to the corresponding Toro math C/M³?

— Absolutely: IF YOU CAN SPECIFY A HOFSTADTER EXPERIMENTAL TOROID ANGLE .. ?

(That would indeed be »stupid» as we [yet], nor Hofstadter, knew What was measured on).

— You were saying .. ?

We calculate the toroid’s transverse ring volume (V) — as »hidden behind the ring surface». From 1 to 360 degrees we set up a 1-360° table on the results, including variable cell-code for entering the Hofstadter’s A¦Z¦C/M³ values for comparison.

TwelvePoints: HOFtoro

• 1. In OpenOfficeCalc we make an A°-table from 1 to 360° in Column A = A°:

• 2. Column B = a, Column C (A=1, A mass number) and D (A>1) gives the above equated toroid top spin partial enveloped volumes,

• 3. so covering the entire transverse toroid ring body’s welV volumetric values 1-360° of its ring section;

• 4. We will »simulate some basic ”electron scattering”» on these partial parts (.. why are you smiling ..), later comparing with the pioneering historical Hofstadter experimental results (1956+ .. Nobel prize 1961 ..) ..

• 5. — if at all (the math here is extensive, not difficult, but it is easy to miss parts .. until thoroughly tested and checked .. and rechecked .. zero flaws ..).

• 6. Column E then calculates the TNED physics Ze/welV as C/M³ (e = 1.602 t19 C, Z connects to the Hofstadter values, in a separate table).

(Column F = TNED:s Column E / T25 ¦ Column G = Actual Hofstadter’s C/M³ divided with TNED:s corresponding in Column F ¦ Column H = Actual Hofstadter C/M³ values)

• 7. The D-section (colD) takes the Hofstadter 1956 results associated AZ (mass number A, nuclear charge Z).

• 8. We use »the 1900s traditional proton gravity circle radius» (HANDBOOK OF PHYSICS, McGraw-Hill series) r0 = 1.37 Fermi = 1.37 t15 M as the basic (neutron) proton A=1 toroid aggregate — securing our here related physics reference (TNED) to be the unique testing foundation (»exact nuclear physics, very, never before seen» ..).

• 9. In a separate HOF-table we have the 13 (from Hofstadters Nobel prize lecture) atoms in his experimental group electron scattering (1956+), specified by AZ and C/M²:

— Hofstadter used the unit T19 C/cM³, which we (international MKSA-system) transfer to the equal more unitive International T25 C/M³.

• 10. We connect the HOF-table to our A°-table — by activating an input cell by a number 1-13, the actual Hofstadter atom.

Then we examine our toroid Toro Ze/V with each of the 1-13 Hofstadter’s corresponding C/M³. Where Hofstadter’s (Hof) C/M³-value appears closest to the Toro set, we use that angle value in a separate new HOF table column for a further final comparing calculation (the final TOROID Planck ring rZ/rG examination: atomic nuclear charge distribution).

[That would be on the equation: rZ/rG = 1/M + (1 – 1/M)(1 – sin[A°/2]) in PREFIXxSIN].

N3View: TwelvePoints

Nothing of the kind exists inside modern academic corridors. And we want a safe and secure proof that it will stay put that way, MAC says.

So .. This TEST is all about that: Did the Hofstadter experimental group (1956+) employ electron scattering experimentation on the above?

— Hopefully, this TORO Planck constant Neutron mathematical physics test will reveal a clear NO — or a clear YES. No speculation. No theory.

PointResult: N3View

RESULT:

What the result points to:

ALL NUCLEI:

KingsTwo54:

a · (n→∞) = (n→∞)Gm/r² = G · [m/(n→∞)]/[r/(n→∞)]² = G · (n→∞)(m/r²) ¦ PlanckRING2 ¦ (n→∞)²/(n→∞) = (n→∞)

THE ATOMIC NUCLEUS cannot be compressed: it is already standing at zero.

FOLLOWING THE PRINCIPLES — no theory, no speculation:

m = [m/(n→∞)] · (n→∞) — shows only one way for deduction (PASTOM):

a top (J0) spinning toroid with a first fractal level of transverse (J1) (spinning) rings;

[Nuclear Magnetic Moment, what we know: spinning electric charge]

(J0 + NJ1 = 0: atom is loss free, needs no refill to work);

mass collected in surface area, no volumetric mass distribution:

an infinitesimally thin mass surface where the g-potential (a) approaches infinity;

the fundamental mass-form of gravitation:

the atomic nucleus; The Neutron;

In TNED Planck’s constant h = mcr also defines The Neutron, r=rG the neutron spin gravity circle radius;

h = m(1.0086652u) · c(2.99792458 T8 MS) · r(1.3196610608 t15 M) = 6.62559 t34 JS.

With nuclear rotational spin r-velocity (v=c @r) as a mechanic feature, v outside r exceeds c:

all electromagnetic sensoring outside r=rG of the atomic nucleus becomes eliminated

(we exclude speculation and theory of how this spin-mechanics function operates: Application Spin).

ToroNeutral: PointResult

• outside r=rG the nuclear surface exhibits electromagnetic neutrality;

• Only the central toroid well charge area counts

— TNED says in granting the specified conditions.

• If that is the true physical case, it should be possible to settle by experimental investigation.

NOTE: In MAC these nuclear spin details have, what we know, no representation at all.

rZ = rG means:

The atomic nucleus is on ints largest outside surface electrically neutral (Gray). Only within the gravity circle radius, approximately half the outer nuclear radius, the nuclear (orange) charge shows up, covering on that surface — not the (toroid rotational) volume the surface is pinpointing. Nuclear charge is a surface distributed phenomena. Not a volumetric distribution.

— We can see directly why any experimental approach — unless the nuclear shape understood — will pose more or less corrupted ideas and (partly hard to understand) data.

— Both Modules Mod0(A=1) and Mod1(A>1) have the same gravity circle radius charge extension relative the nuclear well center (rZ=rG). But as these Mod0 and Mod1 have (huge Inner) MORPHOLOGICAL differences, the experiments with electron scattering (Hofstadter 1956+) poses even more subtle problems, unless understood.

• 11. We scan — manually, visually — the 1-360 A°-table for an eventual closest match of the Hofstadter specified C/M³-value, and writes it up in the HOF-table.

• 12. Then we make the final rZ/rG calculation in the rZ/rG column of the HOF-table:

THIS IS WHAT APPEARED OUT OF THE BLUE:

ResultsTable: ToroNeutral

ResultsTable, copied per row:

Tabellen nedan: DE MANUELLT SEPARAT UTTAGNA MATCHNINGARNA — RADVIS, HELA SERIEN — NÄRMAST MATCHANDE HELTALEN I A°

— Vi väljer typ [13], vilket överför aktuella parametrar i cellerna från HOF-tab.No13; resultatet skannas manuellt efter närmast matchning mellan kolumnerna G och H;

— Det A°-värde som står på den raden, förs in i HOF-tabellen nedan i kolumn M. Därefter beräknas b och rZ/rG i kolumnerna O,P på de erhållna A°-värdena i kolumn M.

NuclearSize2023c26.ods — Tabell5 Q181

AutoÖverföringen av HOF-tabellens värden till TORO-kalkylcellerna (Kolumnerna D och G):

How the Cal-cells are programmed to connect the Hof-values to the A° table complex:

NuclearSize2023c26.ods — Tabell5 A182

PREFIXxCOS:

A183; = LETARAD($F$182;$H$182:$L$194;3;0)

B183; = LETARAD($F$182;$H$182:$L$194;4;0)

C183; = LETARAD($F$182;$H$182:$L$194;5;0)

D183; = A183 → konstant AA ; införs automatiskt i TORO kalkylcellerna

E183; = B183 → konstant Z ; införs automatiskt i TORO kalkylcellerna

G183; = C183 → konstant HOF ; införs automatiskt i TORO kalkylcellerna

Stora NUMMERRUTAN kopplad till F182;

HOF-tabellen: $H$182:$L$194

RevisitHofP2: ResultsTable

ComparingExpermental

Revisiting Hofstadter 1956 — Part 2: electron scattering on atomic nuclei: Electric Nuclear Charge distribution rZ/rG — C/M³

first fractal transverse toro rings: Mod0 1H1 only

first fractal transverse toro rings: Mod1 all the others — 2He4 and Neutron(0n1)-Proton(1H1) have (1.038 difference) the same nuclear radii (rG=1);

Nuclear (gravity circle) radius for A > 1: rG = ½r0√A, r0(A = 1) = 1.37 t15 M = 1.37 Fermi.

The (1956) Hofstadter tested 13 nuclei — TNED morphology only:

No spherical morphology.

Nuclear Charge Density (C/M³): The Hofstadter 1956+ 13 nuclides in electron scattering tests.

HOFTable: RevisitHofP2

The HOF-table:

Columns A-L HOFSTADTER C/M³ DATA FROM THE 1956+ PIONEERING ELECTRON SCATTERING EXPERIMENTS

COLUMN M: copied results from ResultsTable Column Q

Columns O,P the results in this presentation;

NUCLEAR ICONS are TNED;

NuclearSize2023c26.ods— Tabell7 H1

COMPILED FROM NuclearSize2023c26.ods — Tabell6 H179 ¦�H37

rZ/rG ¦ P1: = 1/rG0R + (1-1/rG0R)*(1 - COS(RADIANER(M182/2))) ; rG0R = 104.4615242271

rZ/rG ¦ P2-13: = 1/rG1R + (1-1/rG1R)*(1 - COS(RADIANER(M183 ..194/2))) ; rG1R = 14.4282032303

--------------------

rZ/rG ¦ S1: = Mod0/rG0R + (1 - Mod0/rG0R)*(1 - COS(RADIANER(M182/2))) ; Mod0 = 15.0055534995

rZ/rG ¦ S2-13: = Mod0/rG1R + (1 - Mod0/rG1R)*(1 - COS(RADIANER(M183 ..194/2)))

Columns O,P:

TNED Explains — 7 points:

• 1. A most clear cut corresponding Mod0¦Mod1 difference is exposed in the Hofstadter experimentation (Col O¦R¦P; 1H1 Mod0, A=1 ¦ all other, A>1 Mod1).

• 2. Independent of calculating method (M = rG01R ¦ rG01R/Mod0) the 1H1 nucleus exposes close similar values (Row 1):

• 3. rZ = rG = 1. No doubt.

Taking into account that the largest nuclei (83Bi209) exposes a 7.23 times magnified version of the N3m1.08 2He4 nucleus (2He4) [√ 209/4 = 7.228416147]:

• 4. MEANING that the inner HofHIT 1H1 corresponding Mod0 top spinning toroid-well is proportionally enlarged by growing mass number (A),

• 5. the electron scattering pin pointing at the nuclear surface

— hiding the inner toro volume —

• 6. sees MORE

• 7. and HENCE (Column O: A = 4-209) with a growing higher experimental hit value.

— The corresponding Hofstadter (Column L) C/M³ values A = 4-13 are reversed:

• from highest 2H4 (2.56) to lowest 83Bi209 (1.08),

• as also is the general case (independent of volume shape) between Z and mass number (A) with growing nuclear (mass number) volume.

• Z/A as such decreases from 1(1H1) to 0.397(83Bi209).

• The Hofstadter C/M³ decrease from 2He4 (2.56) to 83Bi209 (1.08) is hence natural as such.

However (TNED toro): In compensating — the toroid well — for the larger access to the electron scattering pin pointing nuclear surface, hiding its inner volume, there is A MISSING EXPERIMENTAL ERROR:

• Measuring on the type heavy large 83Bi209 means

• greater precision access to the actual pin pointing toroid surface;

• HOWEVER, as with all the other Mod1 N3m1.08 nuclei:

• Relative to the tiny N3m15 (»HUGE EMPTY SPIN SPACE»), the N3m1.08 nuclei

• exposes a (relatively, much) larger nuclear mass part — that has NOT nuclear electric connection

BUT (possibly) HAS SIGNIFICANT DEVELOPED NEAR NUCLEAR MAGNETIC FIELD STRENGTH;

• The experimental result on all A>1 sees »A Corrupted (Enlarged) version of 1H1».

HofDiagrams: HOFTable

All the 2-13 Hofstadter A > 1 nuclei:

D1: The TNED tori calculated rZ featuring the Hofstadter nuclei (Col H-L) clearly resemble a linear increase: »the bigger, the more accurate access».

D2: The direct rZ/rG equation on the (Col H-L) Hofstadter 2-13 nuclei.

D3: The corresponding TNED nuclear radius (inverted ½r0√A) values of the (Col H-L) Hofstadter 2-13 nuclei.

The Magnification Effect on the Mod1 A>1 atomic nuclei:

D1: From 2He4 (lowest 0.071) to 83Bi209 (highest 0.542), we see a practically linear growth of the rZ¦Hof extension.

The2DM: HofDiagrams

DE TVÅ SKILDA MORFOLOGISKA PREFERENSERNA

För att kunna utjämna det

(»experimentellt enhetliga»)

märkbart experimentellt ogynnsamma morfologiska

• förhållandet mellan

• den tydliga Hof-gruppens (No1) 1H1 fullträff Mod0 (rZ/G=1) och

• de övriga Mod1 Hof-gruppens No2-13 nuklidobjekt,

• finns, vad vi vet, bara en och endast

• en enda tillgänglig principiellt matematisk lösning:

— Vi relaterar samtliga — även Mod1 gruppens 12 nuklider — till Mod0:

• en och samma preferens.

Ursprunget:

2 skilda morfologiska toroidmoduler

Mod0(A = 1 ¦ 15.006) och Mod1(A > 1 ¦ 1.077):

rZ/rG ¦ P1: = 1/rG0R + (1-1/rG0R)*(1 - COS(RADIANER(M182/2))) ; rG0R = 104.4615242271

rZ/rG ¦ P2-13: = 1/rG1R + (1-1/rG1R)*(1 - COS(RADIANER(M183 ..194/2))) ; rG1R = 14.4282032303

--------------------

Normaliseringen:

1 enda slutlig refererande morfologisk toroidmodul:

Mod0:

--------------------

rZ/rG ¦ S1: = Mod0/rG0R + (1 - Mod0/rG0R)*(1 - COS(RADIANER(M182/2))) ; Mod0 = 15.0055534995

rZ/rG ¦ S2-13: = Mod0/rG1R + (1 - Mod0/rG1R)*(1 - COS(RADIANER(M183 ..194/2)))

Vi dividerar ursprungskoefficienten i Mod1, rG/R, med Mod0:

rG/R = rG1R = 14.4282032303 ;

rG1R/Mod0 = 14.4282032303 / 15.0055534995

= rG(A>1) · Mod0

HofEndResult: The2DM

som ger Kolumn S (jämför Hof-originalet i Kolumn P) i HOF-tabellen:

Slutresultatet normaliserat enhetligt på Mod0:

Idealt för TNED:

• alla 1-13 Hofstadters nuklider uppvisar rZ/rG = 1.

Det enhetliga, yttre, topp-toroidspinnets (motsvarande experimentellt observerade) praktiskt nukleära form — alla atomkärnor, alla masstal (A):

rZ=rG

förutsättningen HOF/HOF = 1 = Toro verifierad

Alla atomnuklider ges (i princip »exakt experimentellt») samma laddningsbrunns utsträckning relativt den atomkärnans egengravitella radie (rG).

— OCH NATURLIGTVIS: Finns minsta tvivel rörande det resultatet, om argument existerar som kan omintetgöra ovanstående genomgång, och dess utpekade resultat: lägg fram den bevisningen. Absolut. Vi söker kunskapen. Inget annat.

Sakfel får inte förekomma här.

SCIENTIFIC AMERICAN (SA) Editor in Chief 1993 (TNED Case History Archives), in a responding letter on the reported TNED finding:

— ”»It’ s a little thin»”. No publication. Even this author hid the result — Behind the Bookshelf — for a Year. Deciding to give it another chance, however (after a year, »Lucky us» ..). it started to rain .. and the desert began flowering up. It was only because of the SA articles (May1979 and Aug1987: collisions between spin polarized protons) that TNED was launched. See from TNEDbegin1993.

What we know: The tiny A=1 transverse 3-ring form can not be seen as such in physics (nuclear angular momentum h=mcr cannot be stopped) — however apparently exposing its existence through high energy experiments.

AKSAcollected: HofEndResult

The Alan Krisch Scientific American collected quotes in UH:

———————————————

The Krisch Group Results from SA 1979 ¦ Experimental Confirmations ¦ TNED illustrated Krisch quotes — Collected Quotes

Notera det särskilt: det finns ingen kraft (i vårt verksamma universum) som kan stoppa topp-nuklidspinnet (Application P65 ¦ TanCons ¦ Eres ¦ Conservation of momentum) ..

— Men väl experiment (Krisch 1979+) som kan påvisa dess existens.

(få atomkärnan, protonen , att se ut som i ovanstående vänstra del:

»spinnet kan inte stoppas» .. varför inte .. ? Energilagen: Applikation 312);

(E = hf = mcr · f = mc² = J·f ¦ = mK = mvr, Kepler momentum)

(universal preservation of angular momentum, J)

.. de tre inre transversella toroidringarna: h = mcr, impulsmomentet eller rörelsemängdsmomentet. Eller som det också kallas, det universella verkanskvantumet; Plancks konstant (massa, laddning och spinn) kan inte förstöras (Energilagen). De inre transversella ringarna är (nämligen också) grunden till hela toroidnuklidens härledning.

— Read it and weep.

TNED — ATOMKÄRNAN, A>1 (Amax = 317): Ursprungligen modellerat i Simply 3D av författaren — gratisprogram från Windows 95-epoken. Varför bjuder inte mjukvaruindustrin mänskligheten på (liknande förträffliga) gratisprogram (numera)? Varför bjuder inte Microsoft på ordprocessorn WORD — så att ALLA människor, särskilt de som (idag) är fattiga, ges en rimlig chans: BIDRA TILL VETENSKAPENS vidare UTVECKLING.

— Eller det kanske är så illa ställt, 2026, Microsoft .. att

— » .. naa .. det krävs En VISS TYP av Människa för det .. de flesta SKA ARBETA åt Oss.

— Vi, eliten, sköter uTvecklingen .. Vi är Unika i Tanken .. och så där ..

— .. förbättrat Upplevande .. runda hörn .. Windows 11 .. tycka Bättre .. ».

— Microsoft Corporation Enterprise: Du ville säga .. ?

Testing equation’s end result:

HOF/HOF = 1 = Toro

Perfect Assembly.

BottomLine: AKSAcollected

— The best MAC provision (»MAC survives») would be if this author has made some very serious errors, so grave and fundamental, that the entire result must be rejected, all together:

— A Direct TNED HIT — @1H1. 1956.

— You were saying .. ?

(This was never written).

(We ended up in a Bad Version of Back to The Future ..).

r = rG: Little (»discardable») difference is seen between the two Modulus toroid morphologies in the top spinning toroid form.

The (1956+) Hofstadter group electron scattering experiments revealed the details — not easily exposed.

— MAC: what was expected .. ? .. :

— The fundamental FORM OF GRAVITATION — the atomic nucleus — should be SOFT .. and DIFFUSE .. ?

(Because Instrumentation — »popular lasers» — cannot pinpoint .. what .. ? .. anybody home .. ? ..).

— It is the hardest ever — on the thinnest most possible: no mass over volume. No way.

— MAC is saying .. ?

Compare the WikipediaQuote.

ComparingExperimental ¦

ToroSpinVolAR ¦ FormulaeTEST ¦ HOFtoro ¦ TwelvePoints ¦ N3View ¦ PointResult ¦ ToroNeutral ¦ ResultsTable ¦ RevisitHofP2 ¦ HOFTable ¦ HofDiagrams ¦ The2DM ¦ HofEndResult ¦ AKSAcollected ¦

BottomLine ¦

Physics7: Compiled as Applications Aug2026 —

APARC ¦ FUNTOP ¦ POM ¦ NEONS ¦ GRIP ¦ DEEP ¦ PASTOM

PBref ¦ ModernIQ ¦ EduModulus ¦

The (TNED) foundation of natural philosophy ..

THE FOUNDATION OF RELATED PHYSICS AND MATHEMATICS

PHYSICS 7 PRINCIPLES — WITHOUT THESE: we’re done.

an Aug2026 Compressed short exposition, with further linked details (Swedish version original around y2000, as linked)

ONLY MAC REPRESENTATION. NEONS, No4 (if that ..)

APARC ¦ FUNTOP ¦ POM ¦ NEONS ¦ GRIP ¦ DEEP ¦ PASTOM

State ¦ Equilibrium ¦ Energy law ¦ Mechanics ¦ Gravitation ¦ Light ¦ Matter

1 ¦ 2 ¦ 3 ¦ 4 ¦ 5 ¦ 6 ¦ 7

Related physics and mathematics

PHYSICS SEVEN PRINCIPLES

STATE

APARC — Absolute Physical Reference

1. Statics principle — a change must always refer an equilibrium

(state condition [»meter read-out interval» or »Galilei idealization»])

PROOF: State — no state (no-variation) exists except based on an interval without change.

EQUILIBRIUM

FUNTOP — Fundamental Theorem of Physics

2. Dynamics principle — Physics relates to equilibrium, not to system

PROOF: APARC — physics is variation.

Explain:

Whereas physics contains no state, only variation, there is neither any reference (state) in physics (variation) to refere to.

Our apprehension and description of physics must, hence, relate a definite interval, an equilibrium.

Within general philosophy we (hence) sharply distinguish between

fathom-world (STATE — differential, dx) and phenomena world (VARIATION — difference, Δx). [»QI math»]

• Physics contains nothing such as ”inertial system”. Nothing such exists in physics.

• The laws, if at all, of physics hold For Physical Systems — never IN physical systems.

ENERGY-LAW

POM — Principle of Motion

3. Motion-principle — Impulse (linear momentum p=mv) precedes force

PROOF: APARC — Energy (Force over distance, work, interval) can neither be destroyed, nor created, only implied

An interval (Δd) with optimal variation a=dv/dt must exist to prove a motion. As Δd is indestructible (APARC), so is also the motion. And thereby also the energy (E = Fd = mad: force over distance: Work).

POM1: ELAW:s 1:st main clause: mass cannot be created — because

m in a=am/m=F/m cannot be created because a in m=ma/a=F/a must be presupposed.

POM2: ELAW:s 2:nd main clause: mass can be destroyed (m→γ) — because

m in a=am/m=F/m can be destroyed in that a in m=ma/a=F/a is indestructible (POM1)..

(a=dv/dt in mass is transposed by [±e] induction [COEI] to heat and light through Pair Annihilation — Star Physics).

MECHANICS

NEONS — Newton’s three laws

4. Newton’s three laws — Mechanics, generalized

1. Every state remains until affected (state and foundational inertia) [APARC].

2. A new state is exactly the force realizing it (force-law, F=ma) [POM via a]

3. Inception for a change always evokes the onset of an equally opposed preservation (inertia) [FUNTOP].

[In electro-physics, the law for electric Induction].

GRAVITATION

GRIP — Principle of Gravitation

5. Convergence principle — Gravitation principle

PROOF: APARC — Equal for all matter, cannot be shielded from; independent of time

Gravitation law from centrifugation force F = ma = mw²/r — time independent:

F=ma=(w²/rm₂)·m₂m=(w²/m₂)·m₂m/r=(w²r/m₂)·m₂m/r²=G·m₂m/r².

m = (n→∞) m(n→∞)^–1 = (F/a)(n→∞)^–1(n→∞) = (F/[a(n→∞)])(n→∞) = m’(n→∞) [»QI math»];

(No theory, no speculation: We only explore knowledge on basic mathematical consequences — if at all).

ELECTRICITY AND MAGNETISM

DEEP — Principle of Light

6. Divergence principle — Equal for all matter, can be shielded from; dependent of time

PROOF: A COMPLETE GRIP NEGATION

Explain GRIP DEEP [»QI math» needed: »time independent»], details below from an Jan2025 Ai discussion;

AS F = G(m/r)²

• gravitation (convergence) exposes Time-Quantity Independence. gravitation »sees changes» immediately,

• independent of distance: (in MAC that statement may cause some turbulence .. we are very well aware of that);

AS LIGHT (divergence) depends on time, light (divergence) should be limited to a constant value, never unlimited.

Testing QI=∞ »QI math» identified properties in light physics,

• expressed on the acceleration form

• a = v/t ; at = v = c, the above GRIP DEEP result suggests this type of explaining QI rank:

[a(Gravitation)=∞] · t = ∞ · c ;

BOTH SIDES OF THE EQUALITY exposes a QI (quantity independent) equality (∞ = ∞).

— Then, by the QI transposition principle (from position to value ¦ »from fathom- to phenomena-world», FUNTOP)

(dt 0 t/[QI=∞])

[a(Gravitation)=∞] = c/(t/∞) = c/dt the final expression renders:

a=c/dt=»light's xyz point space absolute acceleration form»;

Result:

• Light (divergence) reflects (or explains) a space point property

(governed by the local xyz point dominant gravitation potential [Reg])

[Reg, resistive (light physics, electric and magnetic fields) elementary gravity (xyz) space point]

exposing an »absolute acceleration» (convergence-divergence) during »dt 0», featuring a »no time at all»;

(details in our human mind property in fathoming physical world phenomena: FUNTOP [»QI math»]);

• Light [divergence: c0 = (√ 1/[4πε0 · t7]), T¦t = 10^±] exposes a (space) STATE condition through a constant (diverging) interval Propagation velocity c(=c0) = s/t;

• »Space (electric) conductivity»;

Application Planck energy — E = hf = mcr · f = mc²:

Divergence energy (mass dissolution [StarPhysics] energy as light and heat [»QI math»]):

dE = dF·ds = dma·ds =dm(c/dt)ds = dmc(ds/dt) = dmc² = divergence energy; E = mc²;

Application Q — deducing the electric charge: Q=√(m/R)(A/dT):

ELECTRIC FORCE-LAW:

F=ma=m(c/dT)=m(c/dT)(RA)/(RA)=Rc(m/R)(A/dT)/A=Rc(Q/r)² | A=4pir² , Rc=1/ε ; F often as F = (1/4piε)Q1Q2/r² ;

Q1 = Q2 ; F = (1/4piε)Q1Q2/r² = (1/4piε)Q²/r² ; Rc/A = (1/4piε)/r²

(m/R)(A/dT) = Q² ; Q = √(m/R)(A/dT)

PROOF 1: R has no mechanical connection. Only electric. m cannot change through mechanical transportation, only by energy exchanges inside closed electrical systems (particle acceleration only). See further details in Planck Equivalents (EXVER).

PROOF2: (dT connects explicitly to the observed mass increase phenomena by electrons in particle acceleration experiments, explained by Induction through Planck equivalents, every single detail; Einsteins theory does not apply — but his equations are similar, »identical», to the Planck equivalents:

Light physics does not connect kinetics. No way [EXVER ¦ LILYC, Light’s Liberty Clause).

(Light paths does not exhibit centrifugation properties, SolarExp1919).

(Light physics is determined by mass influence: gravitation; GRIP forms kinetics, DEEP follows [its] kinematics [Planck equivalents]).

(KINETICS mv, propagation v with mass m included; KINEMATICS v, propagation with mass excluded [vector geometry]).

Q degenerates with a finite T (T for time here) in Q = √(m/R)(A/dT):

Q² = (m/R)(A/T) = (m/R)(r²/T) =(m/R)(rc); Given mRc, the Q changes with r; we know that is not the case in physics;

• Q is a constant with constant mass over constant space (inductive) resistance and (local, gravitationally determined) divergence c.

In MAC no mentioning of the above kind has been found.

No QI math. No Q deduction. No GRIP-DEEP details.

Application Nuclear Spin:

MATTER is commonly summarized as mass, charge and spin (Planck’s constant h = mcr = 6.62559 t34 JS, basic physics from Kepler momentum K = vr with mass: mvr = J, angular momentum; In light physics v = c). In TNED

h is identified with The Neutron, directly by quantity:

h = m(1.0086652u) · c(2.99792458 T8 MS) · r(1.3196610608 t15 M) = 6.62559 t34 JS,

r = h/mc neutron’s gravity circle radius (rG), u in Dalton (1u = 1Dalton = mC12/12 = 1.66033 t27 KG);

WHEREAS (LILYCref) light physics does not connect kinetics, but is reigned by it, the mechanical-kinetical aspect of a nuclear spin follows this feature:

• AS the neutron Planck constant spin (c) is related to the neutron gravity circle radius, the spin velocity at center is zero — full light divergence. And outside r=rG: greater than c. Nuclear (mass object) spin is kinetic, like a real physical top spinning device — unless any genius can disclaim (no offense).

MEANING:

— Outside r=rG the nucleus has no physical sensitive connection to electromagnetic fields:

— The nuclear surface outside the c-spin r-border is electromagnetically shut off:

— The nuclear surface appears electrically neutral outside r=rG — given the spin velocity limit c @rG.

This could (possibly) be tested through the (1956+. beginning from 1949) early Hofstadter pioneering experimental group electron scattering experiments.

(The Hofstadter experimental group Instrumentation is partly described in the free PDF, The Discovery of the Point-Like Structure of Matter, R.E. Taylor, Stanford 2000).

MATTER

PASTOM — Principal (also Principle) Structure of Mass [orig. 2000: Mass Fractal Clause, MAFACE]

7. Mass structure principle — mass destruction (ELAW, POM2) demands one in mass innate existing structure

PROOF: POM2

m = (n→∞) m(n→∞)^–1 = (F/a)(n→∞)^–1(n→∞) = (F/[a(n→∞)])(n→∞) = m’(n→∞) [»QI math»];

Mass consists of an unlimited number of mass elements perpetually dynamically dividing so that no least mass part can be found (and its origin never be spotted: energy law: cannot be created, cannot be destroyed; no beginning).

Explain: principal structure of mass

The validity of the Planck energy form E = hf = mc² demands mass to be disintegrated into that Planck energy forms of light and heat. The only principle way for that to happen (GRIP DEEP: light does not connect kinetics; Q-deduction; Newton’s Third) is:

E = hf = mc² = UQ with U(induction) = L(di/dt);

m = E/c² = L(di/dt)Q/c² — The integral analogy between mass (m) and inductance (L);

m = h/cr = (E/f)/cr = E/crf = E/c(r/t) = E/c²;

As h = mcr is based on mass (m), charge (c) and spin (r),

the only way to disintegrate m into its inherent energy E would be that

charge (Q) consists of ±e and is connected to (mass m by) spin (±s),

— and that is, or defines, (±e) Pair Annihilation (Energy from our Sun).

The Planck energy E=hf f-term (frequency or rotational velocity [1/t]) should relate to the highest possible light frequencies (gamma, neutrino, Application P71) — as it is already well known that light propagates through matter (Compton effect) by decreasing frequency and increasing wavelength; Due to energy losses on the path, m-dissolution Does begin from a highest f-level, no doubt;

The only way to vindicate [E = h · f = h · [f(n→∞)]/(n→∞)] »any highest possible frequency (f)» (Application 72) in a mass destruction would hence (QI math again) rely on

(Planck fractal system)

h = mcr = (n→∞) · m/(n→∞) · c · (n→∞) · r/(n→∞) — a corresponding h-fractal system: h = (n→∞) · h/(n→∞), or simpler

[E/f(n→∞)] = h/(n→∞); E(even the smallest)/f = h];

As the frequency approaches infinity, the h-fractal system (Application 73) secures that also ITS energy level E = hf approaches zero.

In MAC there is only the highest single h-level (Heisenberg’s uncertainty principle). And therefore any fractal idea is rejected because E=hf would demand »unlimited energy» for unlimited frequency, »h constant».

(» .. The Personnel were retarded and never calculated the QI solution .. » .. »low educated» .. ).

PASTOM overrides that MAC limit — and presents TNED: the only possible fractal mass form to be deduced.

MAC:

— You were saying .. ?

LIGHT’S GRAVITATIONAL DEPENDENCY: — see special dialog Jan2025 on that subject (GravitationalRedshift) with an Ai machine;

— Einstein's form for »Light's Gravitational Dependency» reads:

c/c0 = (1 — w²/c²) with w² = GM/r, outside the (spherical mass);

cannot define the nature of c = c0 = 2.99792458 T8 M/S independent of gravitation;

— Schwarzchilds form is (slightly different)

c/c0 = (1 — 2w²/c0²) with w² = GM/r;

cannot define the nature of c = c0 = 2.99792458 T8 M/S independent of gravitation;

— Related physics and mathematics form:

c/c0 = (1 — w²/cc0) with w² = GM/r;

DOES define the nature of c = c0 = 2.99792458 T8 M/S independent of gravitation;

CHEOPS RECTANGLE bd=h² (so termed [ShortHistory] in UH after the earliest known record [in literature] of that math expression):

Light’s gravitational dependency (LGD) bd=h²:

Designations with Cheops Rectangle (diagonal) written inside a circle (how c[x] varies from c0 by v²=c²+w²=cc0, w²[y]=Gm/r):

[x]: c0 b c d 0; [y]: w; hypo-sides LeftRight: b v (c=d, c0–c=b, w=h; bc=w²);

(w/c) = (c0–c)/w = b/d ; w² = cc0 – c² ;

v/c0 = (c=d)/v ; v² = cc0 = c² + w² ;

c² + w² = v² = cc0 ; c² = cc0 – w² ; c²/cc0 = (1 – w²/cc0) = c/c0 ;

SOLUTION (1 part circle, 1 part hyperbola):

[±(c–c0/2)]² = (c0/2)² – w² ;

CIRCLE:

c/c0 = (½)(1+√ 1–4w²/c0²) from c0 to c0/2

HYPERBOLA:

c/c0 = (½)(1– √ 4w²/c0² –1) from c0/2 to 0 ..

Preservation of c0 independent of gravitational potential (w²) is guaranteed by the hyperbolic part.

That extension could never be reached (frankly: »became banned») by the Einstein-Schwarzschild provisions.

POTENTIAL BARRIER — where Q is taken:

PBref: ENERGIZONEN — STÄLLET DÄR Q TAS — Entirely based on Application P76:

PotentialBarriere

PotentialBerrären

IT (PA, Application p78) cannot be deduced by MAC — due to: no Grip-Deep, no-Q, no-Complete-LGD: no QI-math.

(The GPT-5.nano Ai machine rejects Insight: knowledge — completely. See 30Jun2026 ExposedRevelation).

The six principal functional curvatures — all c-dependent 1 2 5 6 reflect THE ENERGY ZONE c(z) = c0/2:

(We cannot, rationally, deduce the phenomenal mathematics behind radioactivity without the energy zone cz math).

(In MAC the lack of that provision is compensated by probability and statistics — »a student’s atomic nightmare»).

(Besides that: PB [»PA»] explains exothermal fusion conditions: nuclei inside each others PB [circumscribed sphere] fuse directly).

PB HAS SIX BASIC FUNCTIONS given by the electric force law (Coulomb Law) parameters F=Rc(Q/r)² ;

WE BESET for functional clarity that RQ=1=c0=4Gm₂=4w² ;

1. c = (1/2)[1 ± (√ | 1–1/r |) ] ; ± breakpoint @c₀/2 = c(z)

2. U = c/r ; ± breakpoint @c₀/2 = c(z)

3. U = 1/r ; approaches endless with r→0 the simplified school book U-physics form

4. w = 1/√4r ; approaches endless with r→0

5. F(c) = c/r² ; ± breakpoint @c₀/2 = c(z)

6. F(G) = w²/c = 1/4rc ; ± breakpoint @c₀/2 = c(z)

-----------------

STABLE NUCLIDES HAVE ALL 1256 STABLE c(z)=c₀/2 ;

Conclusion:

Without these provisions, what we know, any detailed insight into the atomic universe, especially the nuclear part (the final natural humanity energy solution, no doubt), will be out of the question.

— MAC 2026: The provision were better year 1311.

ModernIQ: PBref

———————————————

Light’s Gravitational Dependency ¦ TestingQI ¦ Application Q ¦ BWref ¦ The GcQ Theorem ¦ Compare QI math in related physics and mathematics

• Nuclear charge

IN RELATED PHYSICS AND MATHEMATICS HAS NO VOLUMETRIC EXTENSION. ONLY A TOROIDAL SURFACE DISTRIBUTION

is limited and distributed over a toroid surface out to a maximum in the very close vicinity of rZ = rG (= r).

PREFIXxSIN

-------------------------------------------------

rZ/rG = 1/M + (1 – 1/M)(1 – sin[A°/2])

-------------------------------------------------

b/(D/2) = 1 – sin(A°/2)

When the HOF-table b-values (ColORS) are weighted through the Mod0 toroid morphology, only, the results become »magnificent».

• In a separate check (Angeli globally collected nuclear RMS radii data 2004) the data point at the same principal end result.

(See SummingConclusion).

— We will welcome any argument possibly capable in rejecting the above result as erroneous. Errors are not allowed here.

EduModulus: ModernIQ

NucleusDeduction Dec2025 — NeutronBegin

Mod0 (A=1) and Mod1 (A>1)

Educate us:

— What means the two toroidal ”Modulus” systems?

Case history — HOW THE ATOMIC NUCLEUS APPEARS AND HOW IT IS DEDUCED, TNED says:

Attempting to define a principal (principle) morphology for the atomic nucleus — gravitations most fundamental entity —

this showed up (TNED history from 1993, and further through the developing centuries ..):

• The most CIRCULAR SYMMETRIC compact and tight central for a spinning FORM (morphology, »structural geometry»: form-shape)

(Planck constant, angular momentum: h = mcr, same as Kepler momentum times mass: J = mK = mvr)

• is (DisclaimingArg) based on the (polygonian) number N = 3. Why is that?

— A central 4-ring construct has a larger central opening, and is therefore excluded.

• We can layout a mathematical draft for the N = 3 spin form — without explicitly knowing at all »all the parameters» at once:

— We don’t have to know the entire building: It will (NucelarDeduction) present itself spontaneously through this, as follows and experienced:

• In all mathematical treatise problems, a ZERO DERIVATIVE (how a function, a process, varies) exposes the most compact possible design — of anything;

• Having an initiating math expression of any variable (x), taking its derivative, defines an equation that can be solved

• on the equivalent of being exactly zero: 0: (most often a precision top or bottom in a changing process);

Illustrated Excerpt (SummingAreas): The actual »Morphological provision» — before any further Knowledge.

See the whole solution in SummingAreas

Exothermally beginning from a Dmax (DmaxREF):

(»the secret lies in A Fusion»: from A=1 to A>1 [basic A=2]; K = 2/√3 – 1 = 0.154700538).

[See ToroNuclearBasics; here in PREFIXxSIN: K = 1/T – 1, where T = cos(180°/3 = 60°) = √ 3/4].

(It is all based on the basic Max Planck provision from year 1900 — Planck’s constant h = mcr; the neutron).

(Also termed universal efficacy quantum — but never in MAC recognized as that: the neutron).

(See how the MicrosoftEdge AiCoPilot responded Jan2025 on mentioning h as The Neutron),

Just »following the rest»,

as pouring water from one bucket to another, no breaks: no speculation, no theory.

Just consequential mathematics. THE PICTURE shows up

(after some elaborative spending hours .. not really wanting to sleep .. not at all ..)

(.. it happened several times at different occasions .. suddenly waking up .. the chair I’m sitting in is about to turn over .. because .. »The Pilot fell asleep behind The Wheel» .. very interesting experience .. as long as it happens behind the desk .. on a safe Earth ground):

• The A=1 basic toroid form (Mod0)

• changes to a final A>1 (Mod1) toroid form for all further (exothermal) fusions:

• Specific relations by precise mathematics crystallize out of that Math Body, defining all details by detail.

— See the (more) detailed Dec2025 NucleusDeduction.

(In 2002 »the plot thickened»; THE NEUTRON SQUARE was discovered/revealed: elliptic equations can calculate atomic masses ..)

(for exact comparison with experimentally measured values — see TheResolution).

• No theory. No speculation. No Consensus.

— Just pure consequential mathematics: skeleton .. nervous system .. blood .. heart .. lungs .. There you go.

Perfect Assembly.

Physics7 ¦ PBref ¦ ModernIQ ¦ EduModulus ¦

NUTGOMAD:

NUTGOMAD — NeutronBegin

NUCLEAR TOROID GEOMETRY MATHEMATICAL DETAILS

NucDed ¦ ToroSpinVolAR ¦ ToroidFractal ¦

Aug2026

FURTHER CLARIFICATIONS ON

THE HOLLOW TOROID NUCLEAR GEOMETRICAL MATHEMATICS

———————————————

Sources ¦

Left: The rG extended )¯( volume of the marked orange inner Toroid (Well trough) funnel is 3.3 times less than the total top toroid spin volume, all A>1:

Proof:

Total top spinning toroid volume (Guldin formulae — simple rotational areas and volumes mathematics):

TotV(rG) = 2pi(rG) · pi(D/2)²

= 2(pi)²(rG)(D/2)² ;

-------------------

welV(rG) = 2pi(rG – 4(D/2)/3pi) · pi(D/2)²/2

= 2(pi)²(rG – 4(D/2)/3pi) · (D/2)²/2

-------------------

TotV/welV = [2(pi)²(rG)(D/2)²]/[2(pi)²(rG – 4(D/2)/3pi) · (D/2)²/2]

= [2(pi)²(rG)(D/2)²]/[2(pi)²(rG – 4(D/2)/3pi) · (D/2)²/2]

= [2(pi)²(rG)(D/2)²]/[2(pi)²(rG – 4(D/2)/3pi) · (D/2)²/2]

= 2(rG) / (rG – 4(D/2)/3pi)

= 2(rG) / (rG – (2D)/3pi)

= 2 / (1 – (2D)/3pi[rG]) ; A > 1; D/rG = 1.8613826013 = q;

= 2 / (1 – 2q/3pi)

= 3.305772316 ; CHECKED

CIRCLE ANGLE(A²)-RADIANS(a) ARC LENGTH. Area (A) — Refreshing BASIC Arc MATH:

-----------

A° = s/2pi = ar/2pi

-----------

Arc Length indicates/covers disc Area:

s/2pir = AR/pir² ; AR = pir² · s/2pir = r · s/2 = r · ar/2 = ar²/2 = A°(pi/180)r²/2 = A°(pi/180)(D/2)²/2= A°(pi/360)(D/2)²

Cirkelytan A = ar²/2; aRAD = A°(pi/180); ......

r = D/2 ;

-----------

a(D/2)²/2 = A°(pi/180) · (D/2)²/2 ..

A>1:

TopTORO WELL delimited Volume:

PREFIXxSIN:

————————————————

welV = 2π · (rG – 4(D/2)/3π) · π(D/2)²/2 ; volumetric

= 2π · (rG – 2D/3π) · π(D/2)²/2 ;

= 2π² ·(rG – 2D/3π) · (D/2)²/2 ;

= 2π² ·(rG – 2D/3π) · (D²/8) ;

————————————————

FOR ARBITRARY SECTORS, aRAD = A°(pi/180) ; A° = 0 → 360°

----------------------------------------

welV = 2π ·(rG – [2D/3π]cos(a/2)) · a(D²/8) ; PREFIXxSIN:

————————————————

See further in AppliedToroMath.

Given the related physics and mathematics TNED precision detailed deduced morphology of the atomic nuclei

• for testing on already known particle experimental results and observations (the 1900s+):

HOFSTADTER’S TEST NUCLEI: Pioneering Electron scattering experiments from the late 1950s (1956+):

1H1 2He4 6C12 8O16 12Mg24 20Ca40 23V51 27Co59 38Sr88 49In115 51Sb121 79Au 197 83Bi209¦195

— What FORM was it that the electron masses hit .. ?

GIVEN A FINITE DIMENSION (Size) FOR THE ELECTRON MASS CONSTITUENTS:

The greater the mass form being subject to the scattering smaller particles, the greater resolution in the responding (angular, energy distribution) scattering result.

— The most reliable (closest hits) should be found on the greatest (most massive) nuclei.

— So, for a first general orienting test, we would concentrate

• only on the most heavy nuclei in the Hofstadter experimental group results.

The TNED provision only:

The end picture using the Hofstadter results would (strongly) suggest, unless disclaimed all together, that atomic nuclear charge has a limited provisional nuclear surface cover property.

— The Hofstadter experiments implied volumetric aspect has to be (severely) narrowed down — if the 1956 experiments do have a fair natural framing, TNED says. No speculation. No theory. Just pure explaining consequential mathematics.

See further in Revisiting Hofstadter Part 2.

NUTGOMAD ¦

NEUTRON: — General ¦ NoVolMass ¦ SpinResMech ¦ NucSpin ¦ TheNEUTRON ¦ ResponBegin ¦ TheResolution ¦ LastQuest ¦

15Aug2026

THE ATOMIC NUCLEUS

THE ATOMIC NUCLEUS — in (UH) TNED Related Physics and Mathematics

Strictly by Morphology (Wave Mechanics) — the alternatives and combinations are innumerable .. so .. how do we know .. ? Test NeutronBegin.

Applying »A general Wave Equative Idea» on the atomic nucleus .. may be problematic ..

TNED has another, simpler, solution.

General: NEUTRON

GENERAL UNIVERSAL STATEMENT (already experimentally well known provision)

All physical masses have a gravity central center point

• independent of form and structure (morphology),

• at any instant of time.

The general picture of all matter in our universe is (simplified, ideally) that

• mass as such can be treated as

• homogeneously distributed over its entire volume.

In TNED (Physics 7:th Principle, P7: PASTOM)

MASS, if expected to be disintegrated into light and heat — Planck energy E = hf = mcr f = mc², h Planck’s constant — must not be based on any finite mass-gravity particle physics;

ONLY (here known) way to secure that it will continue to stay that way is to use the strict mathematical formulation of quantity division excluding any smallest finite remaining:

NUCLEAR MASS consists of limitless divisible mass fractions summed by a corresponding limitless number of such unlimited mass parts (Principle structure of mass, PASTOM).

m = (m/[n→∞])[n→∞] : limitless dynamic divisibility. No speculation. No theory. Just plain consequential mathematics. It is — or not all.

NoVolMass: General

• the atomic nucleus, and any of its possible observable parts

• gravitation’s fundamental form

• have no inner homogeneously distributed mass;

• The atomic nucleus exposes no type macroscopic mass inertial momentum:

• Its mass lies entirely in an infinitesimally thin hollow toroidal shell which gravitational feature approaches infinity.

In general mechanics

(integral applications of rotating bodies)

mass inertial momentum exists because any macroscopic mass object

• has mass over volume (and can therefore be integrated).

• The INNER STRUCTURAL FEATURE OF THE atomic nucleus

• has it not, TNED (PASTOM) says.

MEANING:

— General macroscopic (gyroscopic) physics

• cannot be applied (directly) on the TNED related atomic nucleus.

SpinResMech: NoVolMass

We can, though, put up (even a photographic) Momentary Picture from ordinary macroscopic physics where we can SEE a corresponding TNED nuclear atomic.

PROOF:

Illustrating basic TNED nuclear physics and mathematics

Derived from GyroBASICS by Experimentation (Dec2018) in related physics and mathematics

Not easily understood — unless practicing on a real gyroscope, hand-held spinning bicycle wheels, or alike: direct confirmation on angular momentum force vector directions:

Mounting RIGIDLY on the left illustrated Y-plane disc, a FREELY ROTATABLE Gyroscope (G, right) at the AA-points, exactly as the left Y-disc illustrates the G initial angular vector axis direction, so allowing the spinning G-wheel to rotate also freely around the Y-axis AA vertical .. as we rotate (manually) the Y-disc ..

— will bring the G device (rotating friction-less around AA) along with the Y-disc when rotated:

• the depicted J1K vectors intact: they will NOT move— only G around AA will

— with the AA points following the Y-rotation.

(GyroPROOF: G, on its mass-wheel fully spinning-rotating velocity, can freely be moved along its J-vector = spin axis direction — without affecting or disturbing the J-spin. Or horizontally, perpendicular to J. So attempting to rotate G WITH a rotation Y-disc, provided AA supported, will only preserve whatever J-direction G was set on, at the moment the Y-disc started to rotate: G will be seen to rotate around AA against the Y-disc rotation).

So: ONCE per Y-disk revolution, when it returns to its initial position with the given G vector J direction, the above left illustrated vector picture will be seen (3G:s):

MEANING:

• The basic TNED atomic two-fold nuclear-angular momentum directions illustrated in our macroscopic universe: the basic morphological math, for further.

NucSpin: SpinResMech

The PASTOM (Application P7) solution for the TNED atomic nuclear morphology is given as a spinning hollow toroidal ring — as a spinning (most tight) conventional electric toroidal coil:

(J0¦Y is Mechanic, J1¦XZ is Electric .. and that is about the only basic things we can get; »Toroid Nuclear Electro-mechanic Dynamics», TNEDbegin1993):

NOTE:

These conclusive statements, describing the nuclear morphology, are STRICTLY (so) mathematical-Geometrical:

• no speculation. No theory. Just pure consequential mathematics

— or not at all. We will build it from there, as far as possible — or not at all. It counts. Or not at all.

(Including statements we make, based on misconceptions .. or bad navigation .. must be corrected).

• The J1¦XZ part is the actually defining nuclear mass body, its working (toroid electrical) form.

(It is also deliberately so chosen due to the Right Hand Rule: the magnetic electric current feature).

MEANING — general related atomic and nuclear physics and mathematics:

• No spherical morphology. No way. It is excluded in TNED from square one.

TheNEUTRON: NucSpin

SLUTSATS — den som helst utesluter den moderna akademins uppfattning om atomkärnans natur:

För att kunna förklara uppdelningen av materien i värme och ljus, Solfysiken, Planckenergin E = hf = mc², finns vad vi vet, inget annat sätt att härleda massgrunderna än genom en massans fundamentala strukturfysik: PASTOM ¦ P7: en ihålig toroidform baserad på massa, laddning och spinn:

Plancks konstant: h = mcr = Neutronen: gravitationens fundamentalform.

ResponBegin: TheNEUTRON

The MicrosoftEdge AiCoPilot’s response 22Jan2025

— on Informing the Neutron = Planck Constant:

”.. interesting numerical coincidence ..”

— Educative.

— The Personnel in MAC should have made it from the start.

— They didn’t.

As conclusive as this short presentation is (more details below):

— where did it lead?

The black points in the diagram below belong to the (last California 2023 version ) modern academic spherical Weizsäcker water drop nuclear model. Its values lie way outside any reasonable concurring experimental values. As the mass numbers increase, the differences decrease, and — through the decades with further Weizsäcker parametric inputs — the (last 2023) MAC end nuclear theoretical chart picture of the atomic masses approaches the experimentally measured.

— Especially from the lightest atoms: The pure mathematical Planck constant TNED Neutron Square Elliptic Equations reveal the real steel atomic mass proportions — on Related Atomic mass defects, not the MAC Nuclear mass defects: The Atom aspect includes Electrons. The Nuclear aspect ignores Electrons.

No doubt.

See MAC-TNED ComparingHighestMassDefects

TheResolution: ResponBegin

As compiled in Nov2025:

As seen (MAC black dots: Weizsäcker water drop model data — have changed during the centuries with additional parameters to fit the experimental values): Especially on the lighter nuclei, MAC-values are completely out of the question; the water drop model goes bazooka.

— The heavier the nuclide becomes, the lesser the differences to the TNED related ring toroid nucleus.

— In this comparing chart — TNED versus Experimental — we talk differences in mass defect terms with fractions of single electron masses

(no more than max ±0.2me rel. 0).

— While the MAC values aspire to match the experimentally measured values — where the atoms are affected through the instrumental arrangements — the TNED Neutron Square Elliptic Equation solutions are purely mathematically calculated: the atoms are not affected at all.

Further analysis are under evaluation.

The Dec2025 Picture only between TNED and Experimental (HOP¦CoData):

LastQuest: TheResolution

THE BOTTOM LINE 2026:

The 100 billion dollar question is still not answered:

• Which one is »the Exact»?

— Is it TNED — or Experimental .. ?

• If the latter:

— why is TNED — all elliptic equations — so close .. ?

TNED values have no affection on atoms — pure math only.

But experimental values must, no doubt, use ionization techniques to measure atomic masses.

— We would like to know, more by precision, what the additional experimental features entail,

• by more exact quantities, in order to settle the quest.

NEUTRON ¦ General ¦ NoVolMass ¦ SpinResMech ¦ NucSpin ¦ TheNEUTRON ¦ ResponBegin ¦ TheResolution ¦ LastQuest ¦

TUNS: Aug2026 THE UNIVERSAL NATURE OF SPIN

SpinNature ¦ PlanckConstant ¦ NuclearSpin ¦ ToroidFractal ¦ CrimInvest ¦ ComparingExperimental2 ¦ FurtherInquiry ¦ GeneSpin ¦ NoInnerLoss ¦ MutualTRANSVERSEh ¦ PCmain ¦ FEC ¦ NucleusDefinition ¦ SpinPhysics ¦ DisclaimingArg ¦

Nuclear and Atomic Physics in (UH) Universe History

RELATED TERMS AND DEFINITIONS

Planck constant — Neutron details

SpinNature: TUNS

Universe History Nuclear physics and mathematics Archives as of Aug2026:

UniversumsHistoriaAllmnnaSamband.htm#ExplainNUCLEARrZ

Fysikens7Principer.htm#RingMorphology

Fysikens7Principer.htm#SpinExplains

Fysikens7Principer.htm#SpinReason

Fysikens7Principer.htm#Epush

TNED — as explained from the deduced principles:

THE UNIVERSAL NATURE OF SPIN

Lika stora motriktade krafter och moment, tar ut varandra: ±F = 0; ±e = 0; ±s = 0.

Equally large and opposed forces and moments cancel out: ±F = 0; ±e = 0; ±s = 0.

(+e) + (–e) = 0 ;

(+s) + (–s) = 0 ;

DIVERGENCE (centrifugal force) and CONVERGENCE (centripetal force) always — with no here known exception — is associated with ROTATION: Spin. We name it

(angular momentum [mechanics, Kepler momentum times mass: mK = mvr] generally here in UH designated: J)

Sw.: Impulsmoment, eller Rörelsemängdsmoment

ANGULAR MOMENTUM

J = m · vr

= m · K, K Kepler area momentum

MOVING The J-vector direction device in or transverse (right angle) the J-direction does not change or affect the J-vector property or quantity or direction as such. The only way to affect the given J-vector orientation is to introduce an extra outer force TILTING the J direction in either way.

PlanckConstant: SpinNature

PCmain

Spin’s most fundamentally known (1900, Max Planck) universal representation is given by the

PLANCK CONSTANT (h):

h = mcr

= 6.62559 t34 JS; also traditionally termed: universal efficacy quantum

In UH (never mentioned in MAC) also: The NEUTRON

(discovered 1932 by Chadwick) (here in UH: »gravitation’s fundamental atom»)

m = 1.0086652u ; neutron mass

c = 2.99792458 T8 MS ; neutron spin associated property

r = h/mc ; resulting neutron gravity spin circle radius

= 1.3196610608 t15 M: NEUTRON GRAVITY CIRCLE SPIN RADIUS:

= 1.32 Fermi

u = 1.66033 t27 KG, atomic mass unit (1 Dalton), = m(6C12)/12

Concluding the spin concept would be:

• The spin (J) vector and its spinning/rotating velocity direction resembles »the right hand rule» (LAW):

J in the thumb direction, v in the curling fingers pointing direction;

• AS A SO (mechanically) IDENTIFIED INTRINSIC Atomic-Nuclear PROPERTY

• the two (J¦v) cannot be separated; J¦v always appear as an indivisible unit.

NuclearSpin: PlanckConstant

Ccmpare the Integral Analogy between mass (mechanics) and inductance (electric charges in varying motion) — see LILYC

SPIN IS MECHANIC — LIGHT IS ELECTRIC-MAGNETIC

NeutronBegin

FIRST COSMOLOGICAL PROVISIONS BY PLANCK CONSTANT h = mcr = 6.62559 t34 JS with

(Application P75 — Einstein, Schwarzschild, Related) LIGHT’S GRAVITATIONAL DEPENDENCY

(AbsoluteMetrics — frequency and wavelength varies depending on local gravitation; see GPS-example)

(cDIVc0ref: definition of the nature of c = c0 = 2.99792458 T8 M/S independent of gravitation):

• Planck constant h = mcr versus the regular mechanic angular momentum

J = mvr = mK, K = vr, Kepler area momentum (mechanical spin);

• Local physics on h=mcr

(featuring the spinning neutron-proton on peripheral velocity c on the nuclear gravity circle radius, r)

has adaptive c values depending on local gravitation: highest c on lowest local g-potential, c0 preserved internally, cDIVc0ref;

THEORETICALLY by consequential mathematics:

• Moving (ideally isolated) a h=mcr from a high g-region with low c, to a region with lower g-potential and higher local c,

• would inevitably increase — adopt, adjust — the h spin factor from cLOW to cHIGH. And backwards, same change.

What would the (theoretical, consequential mathematical) DYNAMIC (mechanical) reason be for that Suggested Nuclear Local Space Adaptive behavior?

• SPACE as such has no ”hidden inner energy” resources for such a transition between different g-regions.

• But gravitation — mass concentrations — apparently have:

• There is undoubtedly (no theory, just math)

• a higher intensity in Planck energy E=hf=mc² divergence in low g-potential regions than in high.

— So ..

• What is The Dynamics behind the Extra (or reduced) energy provision (different local space c:s)?

TEST ANSWER:

• THE ELECTRIC CHARGE (Q) senses a more its own extensive (regulated by local c) powerful electric field extension IN local c on a low g-potential than a high one;

• Q has more Inductive potential in low g-potential regions than in high.

• Q »can be pushed» — »BY the local c-space itself» (comparing different g-regions).

• PROVIDED APPROPRIATELY ORGANIZED,

• an atomic nucleus can self-regulate its nuclear top spin, adapting it to the local gravitational c-conditions,

• provided equipped with »a push» mechanism (narrowed »laser Q-field»).

If we exclude that possibility, as related in the above, we would have to exclude

(unless willing to adopt magics and mystics into physics, which is not our table in UH)

also the bare existence of h=mcr as a spinning neutron-proton nuclear device:

• the fact that the h-spin (mcr) on c varies in different g-regions.

The Angular Momentum mechanical TNED calculated nuclear spin math results (NuclearSpinResolution):

Result is in local c-units. EXAMPLE: A=4 (2He4); cSPIN on the nuclear gravity circle radius rG (near half the outer toroid extension rT) = 2c/2 = c.

These results — valid in any local h=mcr c-space condition — reflect different gravity-circle radius related (r=rG) nuclear tangential rotational c-velocities, directly related to the actual nuclear mass number (A).

• If, as suggested, the TNED Planck constant neutron-proton spinning nucleus also has

• »the appropriately organized inner mechanic local space c-adopting» provision,

• further alternative-outcomes opens up:

• The Nucleus can have a DIRECT local c-space adaption — overriding the TNED default c-spin result.

or

• The Nucleus can have a DYNAMIC local c-space adaption — making »auto-adjustments» according to the specific internally balanced nuclear conditions.

Here (UH 27Aug2026), if at all, we have no idea of which is which. Just penetrating the (eventual) possibilities (on already spotted consequential mathematics).

(Being strict and fair: The 1956+ Hofstadter electron scattering experiments, DeducingTHErZ, HOF on the Angeli2004 collected data, would suggest that the latter alternative holds — but that is still far from certain, at the present).

Examining the entire TNED Planck constant fractal toroid spin complex:

Scrutinizing the electric(Q)-magnetic(B)-mechanic (spin, s) on the TNED provisions, renders this illustrated resolution, necessary to explain the overall (vector) functions:

— It is imperative paramount important that no — zero — flaws exist in this illustrated composition:

— Its purpose is to enlighten on all the innate details with zero exception — what has been understood:

ToroidFractal: NuclearSpin

We use the rings with proper Numerical designations to illustrate how the entire limitless hollow toroid complex can be grasped and understood. Every electric-magnetic-spin vector detailed should be reflected in this illustrated composition —or not at all.

The basic J0 (jay-ou) represents the actual top spinning h=mcr neutron-proton nucleus, a basic atomic nucleus in this compiled illustration.

— CENTER J1 MIDDLE RING (nuclear charge location) can be related (TNED says) only as the left part ±q ±s shows.

In actual (electron scattering experiments) the actual top spinning nucleus places the narrow transverse toro ring charge band (J1) as if spread out on a toroid limited inner well trumpet surface [ )( ] (which we are attempting to check in comparing on actual experiments, looking for confirmations — or not at all: »TNED died»: for every new opportunity through the examining decades, from 1993, such tests have only strengthen TNED, so far).

— For the ±q ±s construct to hold, the q-line must be divided as illustrated - - - - divided into each second near lying sub ring as a + and a –.

— The appropriate electric and magnetic forces then apply as illustrated: The near ±q attract (limitlessly, endlessly) — while the transverse near magnetic (±s) guarantee a corresponding repel.

— The atomic fractal does not crash on a total E=hf=mc² dissolution — because electric attraction and magnetic repulsion secure a solid functional mechanic limitless fractal nuclear engine. The reader is encouraged to reject that picture, by attempting to find contradictions in the described construct. Searched for. None yet found. Search continues — perpetually.

CrimInvest: ToroidalFractal

Adding the final Nuclear Spin Vignette in this section, exposes a possible explanation to the nuclear toroid spin transverse ring dynamical construct,

• matching the answer to the open question on how (and why)

• the atomic nucleus automatically can adopt its h-spin (h=mcr) to the local gravitationally dominant c-space:

Investigating The Crime Scene ..

• The (J2) spin direction directly favors a smallest necessary central q-line deviation, profitable for generating the necessary q-push on the local c-space g-conditions

rendering our necessary mechanical ring push dynamics to the local g-dominant c-space:

Suspect ..

NOTE:

• Provided that the nuclear c-spin really is limited (the q-central line ends at rG) to the nuclear gravity circle radius only (r=rG=rZ), the acquired c-spinning velocity there at rG entails that

• any part of the nuclear body outside rG

• will have no sense of electric and magnetic feature

• (v>c)

• because the spin is mechanical, and the nucleus has no inner losses, i.e.,

• is completely independent of MECHANICALLY (g-based) TRANSPORTING velocities.

The »not over the rG limit» responsible dynamics was discussed earlier (2025) here in UH on the possible (consequential) nuclear dynamics in

ExplainNUCLEARrZ:

Our Fact on the table, TNED says:

See also further here in Revisiting Hofstadter Part 2 — examining the experimental results from another point of view (Comparing Experimental).

ComparingExperimental2: CrimInvest

Comparing the Experimental backgrounds:

In the Revisiting Hofstadter Part 1 investigation (introducing DeducingTHErZ) we concentrated (left) on the TNED nuclear deduced Planck constant featuring transverse toro ring volume only, comparing its toroid morphology on Hofstadter’s C/M³ charge volume density values.

FurtherInquiry: ComparingExperimental2

In this Revisiting Hofstadter Part 2 investigation we concentrate (right) entirely on the (more probable experimentally touched) TNED nuclear deduced Planck constant toroid top spinning form, comparing on Hofstadter’s C/M³ charge volume density values.

ComparingExperimental:

We make a table with A° angles from 0 to 360, covering resulting C/M³ values over the entire top spinning surface are — featuring its underlying volume to the Hofstadter C/M³ values. For each of the 13 Hofstadter used nuclei, we scan the A°-table for closest match. And from those values, we make a final test on the tabled different values.

— Surprisingly or not, we found that the Hofstadter values do make confirmations in concord with the above illustrated toroid. rZ = rG — halfway over the TNED deduced nuclear toroid body.

GeneSpin: FurtherInquiry

GENERAL SPIN DETAILS — MECHANICS

The top spinning Planck constant neutron-proton nuclear toroid — has no macro-cosmic comparing physics — except in a limited illustrated way ..

COMPARING NUCLEAR SPIN WITH PRACTICAL PHYSICS GYROSCOPIC EXPERIMENTAL SPIN

— The reason: The Planck spin TNED related toroid has no mass over volume — impossible to illustrate on the physical laboratory table: no inertial moment.

SPIN angular momentum — TNED Related MomentumConservation

Atomic Nuclear spin — ONLY ONE PHYSICALLY POSSIBLE WAY TO DEDUCE:

Moving the J/N device in the direction of its vector (←) or perpendicular to that direction, has no effect on the J-vector direction as such: nothing happens.

CONSEQUENCE:

Placing the above transverse J/N device on a J-rotating disc, the (←) J/N directed vector would still point in the same direction, unaffected by the J-rotating disc. Any other case would introduce a change of the J/N vector direction, forcing it to follow the rotation as a fix arrow, cemented to the rotational disc.

• SO: a separate J/N transverse device connected to the J-spin physics, will NOT retain a J-disc fix J/N vector direction: The J/N vector will rotate counterclockwise the v-direction:

HOWEVER — in our real world mechanical physics — the only way to preserve that provision of constancy would

If the v-orbital (J¦Y) rotational spin angular momentum has a transverse (J/N¦XZ) spin angular momentum device in it

• once oriented in a fix J(N vector position,

• the J/N vector direction ..

Continue on SPIN in

Nucleus Definition.

MATTER, materials, ATOMS, work perpetually without any need for energy/fuel refill:

NoInnerLoss: GeneSpin

• no inner losses: no inner resistance, no inner inductance: no INNER inertial properties.

— But, as observed (1900s), atoms, atomic nuclei, expose measurable SPIN: angular momentum:

• The apparent unique NUCLEAR equivalent Planck constant (h) is so directly spin defined.

— In itself, the (h=mcr) top spinning Neutron equivalent has no, what we know, property where ”no losses” are defined or clarified.

MutualTRANSVERSEh: NoInnerLoss

• The only ”no losses” h-way would be

• a transverse — top h-spin directed and canceling opposed — quantified equal h-spin:

PCmain: MutualTRANSVERSEh

J(0K)[Y] + N(J(1K)[XZ]) = 0 ; (nuclear zero angular momentum postulate)

equally transverse opposed quantities (spinning electric-mechanic toroid ring)

The TNED h=mcr Neutron:

The Planck constant h=mcr — The Neutron

h 6.62559 T34 JS = 1.0086652u · 2.99792458 T8 M/S · 1.3196610608 t15 M = Planck’s constant

u 1.66033 t27 KG = mC12/12; 1 Dalton — its numeric FORM often named ATOMIC WEIGHT [ U; m = NUu; N = m/Uu — not used in MAC; see The MOL concept ]

m 1.0086652u, neutron mass mn ¦ me, electron mass 0.000548598u

c 2.99792458 T8 M/S Light’s divergence in free space — [ neutron ] nuclear spin associated property

r h/mc = 1.3196610608 t15 M: NEUTRON GRAVITY CIRCLE SPIN RADIUS: 1.32 Fermi

Mass and charge property:

mn = 1.0086652u ; neutron mass

me = 0.000548598u ; electron mass

u = 1.66033 t27 KG, atomic mass unit (1 Dalton), = m(6C12)/12

mn/me = 1838.6235458387

= 1818 + 18 + 2.6235458387 electron masses;

= 909±e + 9±e + 1.31±e

1818 = central nuclear massif

18 = atomic mass defect (mD) deposit; NEUTRON SQUARE

mDmax = 17.7591044477me, 26Fe56 (HighestATOMICmD)

———————————————

All TNED data from

THEmDchart, Elliptic Equations, Comparing Atomic Experimentally:

See further in (TheResolution)

As compiled in Nov2025

The 100 billion dollar question is still not answered: Which one is »the Exact»?

— Is it TNED — or Experimental .. ? If the latter: why TNED so close .. ?

TNED VALUES HAVE NO AFFECTION ON ATOMS — pure math only. EXPERIMENTAL MUST USE IONIZATION TECHNIQUES TO MEASURE ATOMIC MASSES.

The electric ±e dispositions (first layout) in the Planck fractal rings are organized through Electric Displacement of type

Basic n-p structures determine the nuclear surface status

Resembling an electric toroid coil, the ±s spinning rings with equally distributed ±e charges develop a confluent directed magnetic field — as if all

the rings have same spin direction and same charge polarity. The electric displacement secures a dynamic change and option as is decided by the nucleus itself, depending on circumstances (±e emission and capture; excitation levels). The displacement also (the overlapping ++ and – –) restricts the attracting magnetic force between the ±e rings, at the same time preventing the close ±e rings to self annihilate.

Similar to the nuclear angular momentum zero summing equation, a zero summing force equation between electron charge and nuclear charge magnetism is needed to explain the balance:

FEC: PCmain

THE ATOMIC (The Chemical Connection, further detailed in) FORCE EQUATION:

F(BT) + F(eZ) = 0

As the electron mass quanta (me) is just (neutron → Hydrogen Atom) an extension of the central atomic nucleus, the (»nuclear-atomic») force equation applies equal to all atoms — and can therefore build SHARING CHEMICALLY CONNECTED (molecular) CHAINS: the atom is loss free, needs no refill to work: sum of all moments and forces = 0:

BT-field, Nuclear positive charge generated magnetic field

BK, nuclear magnetic vector (right hand rule)

Independent of the charged electron mass’ motional behavior in the vicinity of its mother nucleus, its J-spin and B vector will force the electron (e–) to pass always trough the nuclear positive well. Then back out again on the below side of that positive nuclear well.

— So each electron mass perpetually exhibits an ORBITAL circulating motion, as attracted to its mother nucleus.

— The mother nucleus can extract, or emit, electrons/positrons depending on conditions: e– is ejected out from the lower well part, e+ from the upper part (experimentally observed 1956, see WuREF ¦ Wu1957 — detailed ¦ IllustratedTNED).

See also the initial TNED Nuclear ICONS explanation to Dia, Para and Ferromagnetism in DiaParaFerroMagnetism; How the ring toro ±e combinations work under different circumstances.

HOW THE SPIN, MAGNETIC AND ELECTRIC PROPERTIES AND VECTOR FORMS COOPERATE, ACCORDING TO (TNED) STANDARD TEXTBOOK (AND EXPERIMENTATION):

Explain vectors:

As seen. Once given the (well established) vector-form-laws for magnetism (moving charge) and angular momentum

(J=mvr=mK, K Kepler area momentum, v=c in Planck constant h=mcr=6.62559 t34 JS), there is but one, and only one single way to understand our TNED deduced toroid top- and transverse spin details — along with appropriate orders of magnetism and electric charge (±e). Direct experimental confirmations (already 1957):

— In particular: see the Wu1957 dramatically revealing experiment (Quoted) showing that electrons are emitted (”preferentially”) in the opposite direction of the nuclear spin (BK¦J0) vector (Cobalt60), and positrons diametrically aligned with that magnetic vector direction (Cobalt58).

— The electron spiraling is known in particular from Earth’s magnetic field (polar regions): incoming electrons (xy motion) spiral towards the N-pole as the B-lines gets tighter. At a specific energy level, the electron flips to an upward out from N-pole — now traveling to the S-pole along the Earth magnetic field lines, where it is flipped again. In the nuclear case, its toroid well is open. The electron can pass through, forming (FEC) a steady »outer nuclear current» provision, confluent with the transverse spin direction — how the nucleus emits, and regains (EC. electron capture) single electron mass quanta.

NOTE: Given these provisions with top- and transverse s-spins: no spherical form can realize the above nuclear organization. Disclaim: the atomic nucleus (Planck constant h=mcr, The Neutron) is NOT a sphere, as though it is claimed (consensus) in MAC.

What we know: none of these (layout) Planck constant toroid ring features can be explained from the idea of the atomic nucleus as a spherical entity.

See also in NUCLEAR MAGNETIC MOMENT, comparing mathematics MAC/TNED.

See also in THE DECAY OF THE NEUTRON ¦ The Neutron’s Zero Charge — how the electron appears and its resulting Hydrogen Atom.

NucleusDefinition: FEC

CONCLUSION:

• Without the fundamental (energy conservation) provision

• a transverse — top h-spin directed and canceling opposed — quantified equal h-spin:

• the atomic nucleus cannot be deduced:

• not at all explained, not related, on the accounted precision data’s credit.

• No way.

SpinPhysics: NucleusDefinition

— Apart from rotating carousels, whirls in gas and liquids .. the spin of the water drop traveling on water .. for a short moment (TheGIF) ..

Is there any (such Y¦XZ) illustrative example in our real macro world mechanics?

— YES — if we allow ”TRANSVERSE” to have any (appropriate) transverse (rotational) normal (90°) direction relative the Y plane top spin:

EXAMPLE FROM GYRO MATHEMATICS AND EXPERIMENTAL PHYSICS (GyroLagenIll)

— in our normal gravity environment:

The XZ spinning wheel precesses/rotates horizontally around a circle in the Y-plane:

Mutually co-working Y and XZ spins:

Detailed in GyroLagenIll.

• This experimental gravity horizontal Gyroscope’s Y-transverse XY spin only works as rotated +90° relative the above illustrated h-ring transverse J/N oriented XY spin:

• The Y transverse XY spin is hence unaltered (however 90° rotated) between the gravity example and our ideal h-provision (the toroid electric transformer coil).

THE ABOVE PHOTOGRAPHED XY-GYRO SPINNING WHEEL Spinning Y-horizontally:

Removing all the friction losses in this elementary gyroscopic kitchen experiment, the twofold gyroscopic spin duality would continue for ever: no beginning, no end (E-LAW).

• If the top Y spin is stopped, the remaining XZ actual gyro wheel spin body drops off, out and away from its suspension point (and wobbles out ..).

ATOMKÄRNANS h-FORM — atomkärnans möjliga upplösning i ljus och värme genom Planckenergin E = hf = mc² (Pastom ¦ P7)

PLANCKEKVIVALENTEN h = mcr = (n→∞)m/(n→∞) · c · (n→∞)r/(n→∞) — ren matematisk konsekvenslogik: inga spekulationer, inga teorier, bara ren väl relaterbar matematik. Om massan ska kunna upplösas i ren Planckenergi (E=hf=mc²) får inga stela partikelformer existera (massan graviterande egenskap upphör helt och hållet, se COEI). Enda sättet, vad vi vet, att uttrycka det villkoret på är genom den ekvivalenta mängdprincipen med »obegränsat antal h-nivåer»: E = h · f = (h/nF)nF · f = hFfF = hf = E;

— c (=c0) = λf innefattar alla möjliga våglängder (λ) över alla möjliga frekvenser (f). I UH som Plancks Strukturkonstant. I MAC havererar den matematiken genom föreställningen att bara den högsta Plancknivån existerar — vilket skulle påtvinga de allra högsta fraktalfrekvenserna i princip oändlig energi. I TNED (det finns en osäkerhetsprincip för varje fraktalnivå, Application 74) gäller istället ekvivalenterna (Kärnspektrum)

E=hf=(h/n₁)(n₁f)=(h/n₂)(n₂f)=(h/n₃)(n₃f)=(h/n₄)(n₄f)=…

E/hf=n₁/n₁=n₂/n₂=n₃/n₃=n₄/n₄=…

Samma energi kan ge obegränsat höga (fraktala) frekvenser (f) genom att massdelningen på underliggande h-ringar inte har någon ändligt slutlig minsta form (h = n · h/n). Ren konsekvensmatematik.

DisclaimingArg: SpinPhysics

— Any existing argument

(searched for, none yet found, search continues .. NeutronDetails ¦ CompiledNuclear)

disclaiming this stated fundamental provision, will remove all meaning from this presentation.

What we know:

• No spherical form can meet the above observed spin conditions;

• Only the ring toroid top spinning transverse ring body toroid form can do that;

• as in resembling a spinning toroidal transformer

• conducting full operational electric current (featuring the transverse h-opposed spin).

ONSET AND INCEPTION FOR A REGULAR ATOMIC NUCLEAR (NEUTRON, Planck RING) DEDUCTION:

The Transverse most compact center — at first:

— The most compact, form-stable, ring toroidal construct has N=3:

— Adding (fusing) such N=3 toroid aggregates to heavier nuclei

• demands a fundamental derivation (zero based math solution)

• for securing a so defined most compact resulting product.

POLYGONAL ARC MATHEMATICS GIVE THE ENTIRE SOLUTION:

A designates mass number: same as number of basic N=3, forming a heavier nucleus

SO GUARANTEED:

• no speculation;

• no theory;

• just consequential mathematics — on given already well known related physics.

— Disclaim:

THAT ONE: We would very much like to witness the revelation of that one.

— Please, if that is possible.

Most Imminent Paramount Important Duty:

— WE MUST

• find any experimental observation

• claiming any result

• against the above outlined,

• certifying we are done here.

— Please.

TUNS ¦

SpinNature ¦ PlanckConstant ¦ NuclearSpin ¦ ToroidFractal ¦ CrimInvest ¦ ComparingExperimental2 ¦ FurtherInquiry ¦ GeneSpin ¦ NoInnerLoss ¦ MutualTRANSVERSEh ¦ PCmain ¦ FEC ¦ NucleusDefinition ¦ SpinPhysics ¦ DisclaimingArg ¦

TAN26: — Morph ¦ QImath ¦ EnergyLAW ¦ EquilibriumBalance ¦ tIndependent ¦ TAN ¦ Provision ¦ TanCon ¦ SpinProperty ¦ TanCons ¦ SpinCon ¦ ANExperimental ¦ TANdetails ¦ MassStructure ¦ FractalTest ¦ Eres ¦ GrantProof ¦

NeMo ¦ rZ ¦ rZSuggested ¦ TheATOM ¦ NeutronDecay ¦

TNED

THE ATOMIC NUCLEUS

Morph: TAN26

Första delen

MORPHOLOGY

Morph — 1 ¦ Eres — 2 ¦ NeMo — 3 ¦ rZ — 4 ¦

QImath: Morph

The conventional modern academic idea of mathematics on the level of ”sometimes one writes dx for Δx” (quote from Sw. ed. The Crescent Dictionary of Mathematics 1962) completely destroys every aspect of understanding the natural intelligible Idea of math.

The explaining simple QI concept was never mentioned in MAC. See further in FUNTOP.

Modern academic ideas lock the student into a prison of low educated intelligence. Proof:

The (»d ..») Differential (dx = x/∞) is the (xyz position) form for 0

The Indestructible interval (Δx = x/[n→∞]) can never reach 0

THE QUANTITY INDEPENDENT (QI):

Never mentioned in MAC — perfects integral calculus explanation and understanding

QI = ∞:

∞ + ∞ = ∞; A∞ = ∞ ; ∞^A = ∞ ; ∞^∞ = ∞ ; ∞/∞ = 1 ; [1/∞ ||) 0] = [dx = x/∞ ||) 0] ..

(QI-applications)

(Develop the DIFFERENTIAL EQUATION [dy/dx] by purpose of isolating [as much as possible] the x-variable POSITION FORM dx=x/QI; THEN: TRANSPOSE from Positions to Values-Quantities— where x/QI → 0; all dx terms vanish: no need for ”infinitesimal” ideas. And what is left is the derivative [or integral] solution).

———————————————

QI applications ¦

EnergyLAW: QImath

The energy law

An interval (Δx) must exist to prove a motion (v=d/t). Motion, as initiated by an acceleration (a=v/t; = dv/dt) of a mass (m), is realized through a force (F=ma); As the interval is indestructible, so is alkso the motion (0 to d), and thereby the energy (E = mad):

ENERGY CAN NEITHER BE CREATED, NOR BE DESTROYED, ONLY BE IMPLIED. No begin. No end.

———————————————

ENERGILAGEN ¦ Energilagen detaljerat

EquilibriumBalance: EnergyLAW

References for handling physical action and reaction

EQUILIBRIUM AND BALANCE determine the readout of a physical instrument (momentary sample):

• there are no inertial systems in physics (FUNTOP), only momentary readouts based on equilibrium principles:

• physical laws (if such exist) hold FOR systems — never IN systems.

• general preference for light physics: local dominant gravitational potential (Reg).

———————————————

INERTIA ¦

Fysikens 7 principer

GRIP (gravitation principle: mechanics), DEEP (divergence principle: light physics)

Special QI applications

LIGHT AND GRAVITATION

CONVERGENCE PRINCIPLE: gravitation (gravitation principle, »GRIP»):

• equal to all matter, cannot be shielded from: HENCE time INDEPENDENT:

— well known properties.

PROOF — deducing Newton’s law of gravitation:

F=ma=mw²/r=(w²/rm0)m0m=(w²/m0)m0m/r=(G=w²r/m0)m0m/r²=Gm0m/r²; m0=m;

F = G(m/r)²:

• Gravitation F = G(m/r)² — is time independent, which was to be proven.

DISTANCE (r) as such has no time aspect. Neither has mass (m) or the universal G-constant.

DISTANCE can mean space between two atoms — as well as between two galaxies: time independent.

tIndependent: EquilibriumBalance

GRAVITATION PROPAGATION IS TIME INDEPENDENT.

♦ Testing QI=∞ identified properties,

• expressed on the acceleration form

• a = v/t ; at = v = c, the above GRIP DEEP result suggests this type of explaining QI rank:

Application P61:

a = c/dt — light’s local dominant gravitational fix xyz space point divergence

[a(Gravitation) = ∞] · t = ∞ · c

• Both sides of the equality exposes a QI (quantity independent) equality (∞ = ∞). — Then, by the QI transposition principle (dt↔0↔t/[QI=∞]) [↔, Alt+29]

[a(Gravitation)=∞] = c/(t/∞) = c/dt the final expression renders:

• a = c/dt = »light's xyz point space absolute acceleration form»;

Result:

• Light (divergence) reflects (or explains) a space point property (governed by the local xyz point dominant gravitation potential [Reg]) [Reg, resistive (light physics, electric and magnetic fields) elementary gravity (xyz) space point] exposing an »absolute acceleration» (convergence-divergence) during »dt ↔ 0», featuring a »no time at all»; (details in our human mind property in fathoming physical world phenomena);

• Light [divergence: c0 = (√ 1/[4πε0 · t7]), T¦t = 10^±] exposes a (space) STATE condition through a constant (diverging) interval Propagation velocity c(=c0) = s/t;

• »Space (electric) conductivity»;

LIGHT PROPAGATION IS TIME DEPENDENT.

Proof and FIRST APPLICATION:

Proving-Testing LIGHT ENERGY math: E = Fd = m · a · d, mass · acceleration · distance (s):

---------------------------

through a space point (ds) as limited by dt (=c/a), Light's space point Divergence:

E = F · ds; dE = dF · ds;

dE = dF·ds = dma·ds = dm(c/dT)ds = dmc(ds/dT=c) = dmc² = point space light's divergence energy;

dE = dmc² ¦ = E/∞ = (m/∞)c² = E = mc²; Then it holds that:

♦ Over a definite interval;

E = mc² — a complete mass energy destruction into light and heat (electric energy).

• We distinguish Light's Divergence (local space point property) from Light's Propagation (mean speed over distance).

• Same expression through the Planck constant h = mcr with the Planck energy E = hf and c = r/t = rf (»laser speeder»);

E = mcr · f = mcr · 1/t = mc · (r/t=c) = mc².

However, the mc² expression is more simply deduced directly from Planck constant (h = mcr):

h = mcr; E = hf = mcr f = mcr/t = mcc, Planck (light) energy equivalent;

h = mcr = 6.62559 t34 JS, = the neutron: h = 1.008652u · 2.99792458 T8 M/S · (r=h/mc = 1.32 Fermi: neutron gravity circle radius in related physics. never mentioned in MAC)

TAN: tIndependent

THE ATOMIC NUCLEUS — The Planck RING h = mcr

only one way to deduce it — says The Energy Law ..

All the 2026 summing conclusions in TNED:

There is only one way to explain, relate and deduce the atomic nucleus

No Spherical parts or ditto Morphology — basic physical conditions: all derived from and related to Planck constant h = mcr

THE ATOMIC NUCLEUS — its universal fundamental

Sum of all moments and forces = 0: no losses, no refill

The loss-free atomic nucleus demands two mutually opposed transverse (J spin) angular momentum

• to satisfy the possible Planck energy E = hf = mc² mass dissolution into light and heat:

• J(0K)[Y] + 3J(1K)[XZ] = 0

• The only available most compact and tight nuclear morphology realizing that condition is

• a top spinning toroid ring (J0) and its (J1) transverse nullifying ring spin;

• All other morphological candidates will be excluded on that J premise: SPHERICAL NUCLEAR PHYSICS IS EXCLUDED.

Provision: TAN

Finding the morphological mathematics for its deduction is based on the most compact centre polygonial arc composition N=3. It is followed by a fundamental derivation (on zero provisions)

• for certifying that: The fusion between two N3 asserts the most possible compact energy effective resulting (N3+N3) ring toroid, with still further N3-fusions to still more massive toroids.

BASIC UNIVERSAL PROVISION: Planck constant, h = mcr = 6.62559 t34 JS = the NEUTRON:

THE NEUTRON — a Planck Constant Equivalent

TanCon: Provision

GENERAL CONDITIONS:

Given the Planck Energy connection E = hf = mcr · f = mc²:

• atomic/nuclear mass by principle can be converted to light and heat (Planck energy E = hf).

NUCLEAR CONDITIONS:

— As the atom/nucleus does not need energy refill or powering up to continue to work, its internal losses are zero:

• sum of spins (±s) are zero, and sum of charges (±e) are also zero: no losses, no need for refilling.

— WHAT WE KNOW: The apparent only way to DYNAMICALLY ZERO balance a top spin (J0=h) is by

• the existence of a transverse (–J1) J0 counteracting spin:

SpinProperty: TanCon

NUCLEAR SpinNature

J(0K)[Y] + 3J(1K)[XZ] = 0

TanCons: SpinProperty

With these dynamically contra acting spin agents continuously at work, the Atomic nucleus (the entire atom) is already standing on a net Zero

— »just waiting to be Planck energy E=hf dissolved»: already @0.

CONSEQUENCE:

• Deducing the atomic nucleus by principle

• demands two contra acting spin vectorial agents — so vindicating a possible E=hf=mc² nuclear dissolution: heat and light.

• That leaves us, what we know, with only one resulting possible atomic nuclear morphological solution:

• a toroidal RING — with a transverse (fractal nature) underlying ring structure (Planck structural constant):

• no spherical parts. No way.

A most compact possible toroidal ring, most tightly assembled for most effective dynamics over least possible resistive/inertial paths

— with a well defined transverse connection.

SpinCon: TanCons

The most compact and fundamental toroid (Planck Ring, fractal) form is this,

as deduced by every detail:

N3m15

ANExperimental: SpinCon

MEANING:

• the one and only physically (Planck constant detailed) atomic nuclear form

• available in any electron scattering or other particle experimental investigation

— unless so disclaimed by any physically or mathematically related available by any means argument: no spheres; no constituent particles.

— Works like splashed water — fully separate individual drops (nuclear particle physics) — merging back to a unitive substance: no moving internal particles.

• WITH THIS PROVISION, WE CAN (NOW, FINALLY) EXAMINE ALL PREVIOUS PARTICLE EXPERIMENTATION ON THEIR STATISTICAL ACCOUNTED DATA.

TANdetails: ANExperimental

Q — härledningen

Ljusets gravitella beroende

Potentialbarriären — hur Q TAS, elektrofysikaliska grundbegrepp, principalpartikeln

Planckekvivalenterna

THE ATOMIC NUCLEUS

— its fundamental deduction

r = r0½√A ¦ NuclearSpinDeduction — as rG: gravity radius

Toroidal gravity circle radius, A>1, massnumber: r = r0 for A=1: r0 = proton radius, 1.37 Fermi: »OldSchool» 1900s;

rT = Toroidal extensive radius:

rG/ rT = 0.502404736 for A = 1: INV 1.990427097 1.99 — See m0 ¦ m1

rG/ rT = 0.517949192 for A > 1: INV 1.930691302 1.93 — See ToroNuclearBasics Dec2025

Ultimate Provision— or not at all:

All Planck Ring terms are related to

— OR MUST SO BE RELATED TO —

the gravity ring spin circle radius

r = rG (Planck constant neutron original: 1.32 Fermi):

PLANCKRINGEN — TOROIDFORMEN N3m20, SA från Maj1979; HOP 1967 (Kubgrafen) — DEUTERONEN

MassStructure: TANdetails

• Utgångspunkten med Planckenergin E = h f = mcr f = mc²

— kräver (P7 ¦ PASTOM, priniple structure of mass) att massan (atomen, atomkärnan) inte får innehålla stela partiklar:

• massenergins fullständiga sönderdelning i ljusenergi kräver ett fraktalt system av massa, laddning och spinn;

(COEI, conservation of energy by induction — Integralanalogin mellan massa m [v] och induktans L [i]);

(E = hf = U[source] · Q[target]; U = Ri = Rt · i/t = L · di/dt; L inductance; initiated by pair annihilation: ±e);

• Plancks konstant h = mcr = 6.62559 t34 JS definierar (impulsmomentet: universella verkanskvantumet),

— rörelsemängdsmomentet (Eng. Angular momentum J = mvr, vr = K = Keplers ytmoment);

• neutronen (gravitationens atomära/nukleära fundamentalform):

h 6.62559 T34 JS

u 1.66033 t27 KG = mC12/12; 1 Dalton

m 1.0086652u, neutron mass mn ¦ me, electron mass 0.000548598u

c 2.99792458 T8 M/S Light’s divergence in free space

r h/mc = 1.3196610608 t15 M: NEUTRON GRAVITY CIRCLE SPIN RADIUS: 1.32 Fermi

mn/me = 1.0086652/0.000548598 = 1838.6235458387 = 1818 + 18 + 2.6235458387 electron masses (±e);

här i (UH) Universums Historia också benämnd

• PLANCKRINGEN (h=mcr);

• nuclear mass and charge

— is consequentially situated in the (fractal, infinitesimal hollow toroidal morphology) toroid surface shell

— gravity definition, see PR2:

• no Q/V, only a Q/A; related:

• no volumetric mass property: related:

FractalTest: MassStructure

• För att rent matematiskt (fysikaliskt) testa/härleda en sådan (fraktal) ringform är vi hänvisade till matematiken (formläran: morfologin) för cirkulära polygonkomplex:

— Hela ringformens kropp sammansatt av X antal tvärställda mindre ringar som sedan (fraktalt upprepat)

• i sin tur består av XX antal tvärställda underringar, som sedan (fraktalt upprepat)

• i sin tur består av XXX antal tvärställda underringar, som sedan ..

— obegränsat, utan slut (Se den enkla beskrivande och förklarande numeriska principen i QI).

HANDBOOK OF PHYSICS, McGraw-Hill 1967; Kubgrafen — Deuteronens radie

• Traditionellt inom partikelfysiken användes (under 1900talet) sambandet

r = R = r0 · A^1/3, r0 = 1.37 Fermi;

approximerade atomkärnans radie via givet masstal A: kubgrafen

HANDBOOK OF PHYSICS McGraw-Hill 1967 ..

Med sambandet för toroidformens radie känt, kunde ett första prövande test genomföras (N3m201993):

• Den approximerade etablerade Kubgrafens ekvation för kärnradien R

• testas mot toroidformens två modulagenter (N [ringantal fraktalnivå 1] och m [ringförhållande fraktalnivå 1]),

• N, antalet underringar i den toppspinnande (Planckringen);

• m, förhållandet mellan N-ringarnas bredd och deras underringars diameter

(som definierar första formmodulen för hela det ringbaserade fraktalkomplexet; se särskilt detaljerad beskrivning i DEDUCTION — men den senare fullständiga härledningen [2025] var inte [helt] känd från början i den här historien, 1993+);

RESULTATET av den prövningen (uppskattningsvis en så nära Toroidform som möjligt som »matchar» kubgrafens nuklidradievärden) introducerade Planckringens neutronekvivalent på Toroidmorfologin

• N3m20.

(Den senare fullständiga 2025 härledningen kunde fastställa en något modifierad version: N3m15).

Eres: FractalTest

Andra delen

ENERGY RESOLUTION

Morph — 1 ¦ Eres — 2 ¦ NeMo — 3 ¦ rZ — 4 ¦

ATOMKÄRNANS IMPULS(moments)EKVATION:

[Y] Y-plane is normal to y-axis; [XZ] XZ-planes are spin-normals to Y;

J(0K)[Y] + 3J(1K)[XZ] = 0

Explain:

• Planck RING angular momentum (J=mK, K=vr = Kepler area momentum)

— relates the toroid ring morphological top SPIN[Y] (J0K).

• The atomic nucleus is free from losses (zero inner electric resistance, zero inner electric inductance: no electro-magnetic changes [spin property changes on (exothermal) fusion, where energy is released; stable atoms/nuclei have constant energy provisions]):

• needs no refill to continue to work on mass, spin and charge, endlessly:

— sum of spins = 0 = ± s; sum of charge = 0 = ±e;

• remaining: mass: m = E/c² from Planck energy E = hf = mc²;

— the entire atom/nuclear mass can be transferred to Planck energy (light and heat);

• all spin parameters cancel (±s = 0); all charge parameters cancel (±e=0);

• all mass properties — gravitation (Integral analogy between mass and inductance, COEI) — disappear;

GrantProof: Eres

GRANTING a complete Planck energy dissolution of the atom/atomic nucleus as possible, no way the atomic nucleus has any direct resemblance to a water drop — that only so in a most primitive (first test) manner (CubeGraph: r = r0A^1/3):

• the atomic nucleus works as a (twofold angular X¦Y¦Z momentum device) spinning ring (h=mcr ¦ Y).

— Most certainly it is so. If any present argument exists in explaining it is not (searched for, none yet found, search continues), this presentation has no longer a meaning.

(Disclaim this Planck ring h-PROVISION — and this presentation has no longer a meaning).

(It is of the utmost importance that no flaws or errors appear in this basic nuclear draft):

NeMo: GrantProof

Tredje delen

DEDUCING THE PLANCK RING ATOMIC NUCLEUS

The Neutron Morphology

Morph — 1 ¦ Eres — 2 ¦ NeMo — 3 ¦ rZ — 4 ¦

• Seeking the most compact, least resisting on a resulting constant spin property over smallest possible volume, most energy effective angular momentum construct (h = mcr), the toroid ring center will have the smallest possible opening if the transverse: Angular (J1K) spins consists of three rings (DisclaimingArg):

• This is all on credit of a pure (simple conventional classic) polygonial ARC Mathematics:

— and apparently nobody in MAC ever cared to even make a simple investigation on its property, what we know:

• Solving the morphological transfer between the top spin (J0K) and its first fractal transverse (J1K) spin,

• certifying a most compact close solution

• involves an elementary derivation:

— The derivation (»no losses») resembles two A=1 nuclei (Neutron-Proton, or Proton-Proton; neutrons do not unite directly) forming a resulting A=2 (Deuteron) nuclei, summing the two A=1 transverse toroid surface areas to the A=2 transverse one.

The result of the named derivation directly defines

— the entire J0K J1K spin morphology with all their ring dimensional equative properties

• in two different toroid modules;

• The neutron-proton basic A=1 (A, massnumber) nuclear property;

— N3m15;

• all other nuclei A>1;

— N3m1.08.

See the 2025 complete mathematical-geometrical detailed DEDUCTION.

rZ: NeMo

Fjärde delen

ATOMKÄRNANS LADDNINGSFÖRDELNING

Morph — 1 ¦ Eres — 2 ¦ NeMo — 3 ¦ rZ — 4 ¦

HOFSTADTERS TEST NUCLEI:

1H1 2He4 6C12 8O16 12Mg24 20Ca40 23V51 27Co59 38Sr88 49In115 51Sb121 79Au 197 83Bi209

Initiellt finns, vad vi vet, inget som påtvingar Q en r=rZ begränsning

(.. en halv sanning .. vi VET inte riktigt .. än .. 12Aug2026)

Det är bara resultaten från Hofstadter och Angeli

(AtomicNucleus2023.htm#TheAtomicNucleus)

som visat den bilden.

([psi] Ψ-sambandet):

1/[(1/r)³ + (0.0033 T25)(A/Ze)]^¹/3/r₀

——————————————————————————————

1/[1/r³ + (k=C/M³)/C]^1/3/r0 → numeric(r0 Meter):

r0 = Related TNED Toroid Proton Gravity Circle radius 1.37 t15 M (HOPdata1967).

rZSuggested: rZ

Suggested general TNED order:

ONLY THE MOST FUNDAMENTAL:

• Charge Radius Extension = r = r0½√A ; rZ = ½√A = r/r0

• a (Planck ring) Top SPIN central well )( toroid surface extension:

Explain — suggested:

— Because Planck constant (the neutron: h=mcr)

• only collects the gravity circle radius extension dynamics,

• so that the entire toroid top (h) spinning body (rT)

• is only Q=Ze covered up to a rMAX = r0(rZ):

— The remaining Toroid Body is ±e NEUTRAL

(Disclaim this Planck ring h-PROVISION — and this presentation has no longer a meaning).

(It is of the utmost importance that no flaws or errors appear in this basic nuclear draft):

TheATOM: rZSuggested

• The (rZ) Z(e+) Nuclear Well )( is continuously communicating with (electron orbital combinations) its negative ELECTRON MASS spouse,

• through the general force (chemical) equation equivalent

F(BT) + F(eZ) = 0

the atom’s force equation

so that (certified chemistry is guaranteed — in any chemically possible rank)

all (involved) atom share the same electron mass — as a nuclear well constant current (divided between the atomic constituents).

NeutronDecay: TheATOM

Den universellt fundamentala instabila atomkärnan: Plancks konstant h = mcr = 6.62559 t34 JS

NEUTRONENS SÖNDERFALL — 12-14 minuter .. i rymd där c > 0:

Neutronen (0n1) sönderfaller exotermiskt (avger energi) spontant (arbetet till omställningen tas inifrån dess ±e egenmassa) till en protonkärna (p) och dess elektronmassa (e^–): en väteatom (1H1):

Neutronens eget (svaga) negativa magnetiska moment (B) ändras till ett starkare positivt dito:

Neutronsönderfallet

THE NEUTRON DECAY — 12-14 minutes

mn(1.0086652 – (m→γ)(0.00084001) = mp(1.007276592) + me^–(0.000548598) = 1H1(1.00782519)

(m→γ)(0.00084001) = (me = 0.000548598) + 0.000291412

— In order to relieve one q into an outer electron cloud, one q mass must (also) be used (+ some extra) as Planck energy work (E=hf=mc²).

The Neutron does that.

ATOMIC MASSES IN u UNITS [1 Dalton = u = 1.66033 t27 KG] = Atomic Weights

mn – [(m = [ (me = 0.000548598) + 0.000291412 = 0.00084001]) →γ] = 1H1(1.00782519)

AFTER (12-14 min) HAVING REMOVED INTERNAL MASS FOR THE REBUILDING WORK (m→γ),

the Neutron has become one Hydrogen Atom.

Small unstable negative magnetic moment .. to a stable positive ..

• Regular electro-magnetic fields and their properties (dia, para, ferro) are fully explained from this nuclear-electron symbiosis feature.

(Disclaim this Planck ring h-PROVISION — and this presentation has no longer a meaning).

(It is of the utmost importance that no flaws or errors appear in this basic nuclear draft):

TAN26 ¦

Morph ¦ QImath ¦ EnergyLAW ¦ EquilibriumBalance ¦ tIndependent ¦ TAN ¦ Provision ¦ TanCon ¦ SpinProperty ¦ TanCons ¦ SpinCon ¦ ANExperimental ¦ TANdetails ¦ MassStructure ¦ FractalTest ¦ Eres ¦ GrantProof ¦

NeMo ¦ rZ ¦ rZSuggested ¦ TheATOM ¦ NeutronDecay ¦

RanBam: RadioBase: — Compiled Aug2026 from previous 2017 — tIntegral ¦ kFactor ¦ RAA ¦ tHproof ¦ log2Fractal ¦ INSERTINGk ¦ NUCLEARb ¦

RADIOACTIVE NUCLIDE BASIC MATHEMATICS

RadioBirth ¦ StabUnstab ¦ E1818 ¦ bcz ¦

TNED related details only

E1818 nuclear related physics and mathematics

Related physics and mathematics explains

RADIOACTIVITY — E1818

LIBERATION OF STUDENT’S WORST NIGHTMARE:

full explanation of the nature and mathematics of radioactivity — TNED says: disclaim.

Related physics and mathematics

INTRODUCTION in SAMEXRAM — background terms

Ideal Homogeneous energy influence: Planck (energy) fractals: E = hf = (h/[n→∞]) × f [n→∞] .. unlimited Planck frequencies f on limited Planck energy E

THE FOUNDATIONAL MATHEMATICS OF RADIOACTIVITY — h/[n→∞] = c × mr/[n→∞]; h = mcr, E = hf = mcr f = mcc.

The Planck energy NUCLEAR RADIOACTIVITY (E=h·f=mcr·f=mc²) INTEGRAL

THE EXPONENTIAL ENERGY FORM — nuclear radioactive mathematical physics, fully related

CompiledAug2026

Related physics and mathematics, Aug2026

RADIOACTIVE NUCLIDE BASIC MATHEMATICS

Detailed TNED deductions and explanations

1 2 3 4 5 6 7 8 9 10 11 12 13

tIntegral: RanBam

NUCLEAR CHARGE STABILITY and instability can be examined an tested through the Planck constant (h=mcr; Kepler mass area momentum, mK=mvr=J) energy equivalent

E = hf = mcr/t ;

----------------------------------------

(1) E = J/t ;

(2) E/J = 1/t ; a Time-Frequenzy function

(3) UQ = J/t ; Planck(mcr)¦Kepler(mvr)

= mvr/t ; E = mv²/2 ; 2E = mv² ; √2mE = mv ;

UQ/mvr = 1/t ;

(1V/M)Ze/mv = 1/t ; Z-related RAA criteria

= (1V/M)Ze/√2mE ; RAA, radio active atom

Integrating the Planck-Kepler fractal TNED nucleus (1V/M)Ze/√2mE over all its possible fractal nuclear frequencies (f=1/t, = [n→∞] · f · [n→∞]^–1 ¦ QImath)

(until the unstable condition ceases and a stable condition is established: »no more frequency deliberation»: applies only for unstable atomic nuclei)

we receive a time (frequency) constant:

— The energy (rank’s right side) associated with THAT integration (accumulated f:s during a time interval t) can only, what we know, pertain to .. the individual (specific family of) nuclei with the given parametric connections (ZE):

(Half-life t = tH is Quantity Independent .. holds for few as well as for many .. all ..)

(4) d(E/J) = dt(t + 1S) ; .. + 1S for a normalized definite integral solution

(5) d(E/J) = [t=t→0]dt(t + 1S) ;

(6) E/J = ln(t + 1S) ; definite integral: x = t = 0 defines y = ln1 = 0.

= (1V/M)Ze/√2mE ;

kFactor: tIntegral

1/(t + 1S) · dt = ln([t + 1S]k);

Log5: Dn ln(P) = Dn(P)/(P); Dn ln[(t+1S)k] = Dn (t+1S)k/(t+1S)k = 1/(t+1S);

— We are allowed to — arbitrarily — add a constant (key) k to the ln(P) form — as it any way »has no existence» in the integral’s derivative (variant) form.

Log5: Dn ln(P) = Dn(P)/(P); Dn ln[(t+1S)/k] = Dn (t+1S)/k/(t+1S)/k = 1/(t+1S);

— Anyway we can suit it — then examining where it leads to .. (there are many possible solutions ..). The exponential of the logarithm solution then reads:

(7) (t + 1S)k = EXP[(1V/M)Ze/√2mE] ; EXP = e^ ...

= EXP[UQ/mvr] ; normalizing exponential unit on physical constants:

= EXP[1SUQ/mvr] ;

= EXP[1S(1V/M)Ze/√2mE] ;

RAA: kFactor

t RAA Quantity Independence 1:

Radio Active Atom, RAA (Z-specific)

A counter-clock frequency Quantity Independent: t.

• Holds for every specific Z-related RAA — radio active atom family

• independent of RAA quantity: one and the same t value.

k .. = .. ?

CONDITIONS:

— The t-solution holds independent of whatever number of Z-related RAA:s remain, as that amount perpetually decreases from unstable to stable atoms;

What connects the RA energy integral constant (t) — independently to the

number of remaining Z-characterized RAA:s as these perpetually decrease in number?

There is but one single unique number (logarithmic) system that connects: ²log.

tHproof: RAA

Proof Exemplified — »quantity independency»:

tQuantEX: tHproof

After ½ of 1 — is ½ left .. starting again from ½ ..

ALWAYS LEAVES A PROPORTIONAL SAME REST.

Same condition apply on every new halving:

• remaining quantity: quantity independency secured.

------------------------------

Compare:

------------------------------

After 1/3 of 1 — is 2/3 left .. starting again from 2/3 ..

LEAVES disproportional RESTS AS DIVIDED BY 1/(≠2).

Same conditions does not apply on every new 1/(≠2) division:

• remaining quantity: quantity independency distorted.

------------------------------

Conclusion:

• The t-energy solution

• demands a complete homogeneous quantity independence: ½ ;

• no change on energy influences and activity decay on the remaining RAA:s:

CONCLUSION:

The t-energy solution demands a halving ½ numerical spouse for preserving the t-energy solution quantity independence;

log2Fractal:tQuantEX

²log Fractals:

N = N0/2^T = N0 – t/2 ; t = 2(N0– N)

T = (ln[N0/N])/ln2 = (1/ln2)(ln[1+t/2N]); t real = T·tH ¦ T=1

t real/tH = (ln[N0/N])/ln2 ;

t real/(ln[N0/N]) = tH/ln2 ; CHECKED

Every other number base than ²log distorts the t-integral’s quantity independent Z-related RAA criterion.

INSERTINGk: log2Fractal

k = 1/ln2

t = tH

The final t-integral solution (t = tH, half life constant of the Z-related nuclear RAA family:

(8) 1S+t_H = 1Sln2e^UQ/mvr ;

1S+t_H = 1Sln2EXP[UQ/mvr] ;

1S+t_H = 1Sln2EXP[(1VS/M)Ze/√2mE] ;

ln2 = ln[N₀/N]/T ;

T, number of tH:s ; N₀/N = 2^T the heart of the matter ; ln(N₀/N)/ln(2) = T:

The added b-coefficient connect to the electric force equation (e = Q)

(8.1) 1S+t_H = 1Sln2e^B/p ; also the MAC Geiger-Nuttal form

(9) 1S+t_H = 1Sln2EXP[(1VS/M)bZe/√2mE] ; b = 4πÑ

b-connection:

F = (1/4πε₀Ñ)(Q/r)² = (Q/4πε₀Ñ)Q/r² = (Q/4π[D/Ξ]Ñ)Q/r² = (Q/b[D/Ξ])Q/r² = (Q/[D/Ξ])Q/br² ; Fr = E = (Q/[D/Ξ])Q/br = (ΞQ/[D])Q/br = .. no .. won’t work .. elp ..

(10) b = 4㥠; numeric

Ñ ±max = 2 ;

(11) Ñ = 1 FOR ALL STABLE NUCLEI ;

(12) t_H/ln2 = 1Se^bZe/√2mE ; omitted ”+ 1S”

(13) b = (√2mE/Ze)ln(tH/1Sln2) ;

— This b-coefficient was the one central in order to explain the entire nuclear radioactive mathematical physics: the TNED nuclear surface charge DISSONANCE — on credit of the potential barrier (Application 78): the energy zone (cz), where Q (Application P63) is taken — by principle: No MAC mentioning.

NUCLEARb: INSERTINGk

b = (√2mE/Ze)ln(t_H/1Sln2)

m, Alpha particle mass, E Alpha particle ejected energy, Z radio active nuclear charge, tH half-life in seconds of the Z-related radio active nuclide family.

— b: »nuclear capacitivity», 4pi for all stable nuclei.

— e: electron quanta 1.602 t19 C.

b cannot be calculated directly. It can be determined only from measuring the half-life (tH) and the Alpha particle (E) energy ejection from the given Z-related radio active atom — m the Alpha particle mass.

RanBam ¦

tIntegral ¦ kFactor ¦ RAA ¦ tHproof ¦ log2Fractal ¦ INSERTINGk ¦ NUCLEARb ¦

SAMEXRAM: CompilationAug2026 [ from 2017]

StableUnstable ¦ SchemIllustr ¦ NuclearInstability ¦ bCoefficient ¦ JApplication ¦ pApplication ¦ ElectricForceLaw ¦ bCo ¦ SimpleEnergy ¦

TNED related details only

E1818 nuclear related physics and mathematics

STRUCTURAL MATHEMATICS EXPLAINS RADIOMATH

— The Statistical Probability approach can come along too. But it is superseded by a (more) detailed related explanation, same practical end result.

StableUnstable: SAMEXRAM

Using the seemingly only possible opening for relating the difference between stable and unstable atomic nuclei — the energy-zone c(z) property (Application 78):

— Unstable atomic nuclei exposes charge density (Q/A) (TNED Planck constant nuclear surface pressure) fluctuations:

— These Planck constant nuclear details have no established references, what we know.

SchemIllustr: StableUnstable

y = 0 + (0.1x)(sinx³) ¦ PREFIXxSIN ——————— x=sine; y¦=cosine:

Frequency modulated and increased Amplitude wave morphology.

See also the schematically related details in R-function

The preferred illustrative interpretation.

— Nuclear instability begins from the highest possible frequencies (Compton effect), with lowest possible energies (RadioBase), evolving to lowest (E’’ [= hf = h/∞ · ∞f] → 0).

NuclearInstability: SchemIllustr

UNSTABLE NUCLIDES (Alpha radio nuclides) exposes fluctuations in c(z) = ç (»ce-dilla») until stable; ç/c(z) <> 1 ;

Because Charge Density D=Q/A=ε₀Ξ=Ξ/Rc is (electric and magnetic polarization phenomena), what we know, the only possible fluctuating nuclear physical (sourcing) factor to which nuclear instability (work — losses — is needed to maintain the unstable condition [»hammering industry»]) can be addressed — leading to a future split of the nucleus (aspiring to find a stable condition, giving off infinitesimal work energy [dissociation, preparing a nuclear rebuild] until a break through occurs).

-----------------

h = mcr = n(m/[n→∞]) · c · n(r/[n→∞]) : STRUCTURAL MATHEMATICS ON PHYSICAL CONSTANTS AND UNITS:

E = UQ = Fd; U/d = F/Q = Ξ, electric field strength (here Greek Xsi); E energy, F Force, d distance, U voltage, Q charge.

Coulomb law (electric force law) F = (1/4πε₀)(Q/r)² ;

-----------------

b = 4πÑ ¦ natural Q(e) associated coefficient

TNED (Planck structural constant) EXPLAINS7relates RADIOACTIVITY MATHEMATICS:

It is connected to the atomic nuclear (beginning from The Neutron) charge density dynamics

bCoefficient: JApplication: pApplication: NuclearInstability

tIntegral ¦ tHproof ¦ bKOFF ¦ Application P78

b-coefficient (bcz) from the electric force (Coulomb) law:

(»nuclear capacitivity»)

Ñ (n-tilde, Alt+0209) = 1 for all stable atomic nuclei.

Ñ = ±<1> for all radioactive (Alpha) nuclides

[Max Ñ = ±2, separate analysis: Alpha energy and t½ measures will clarify this terminology]:

F = (1/4πε₀Ñ)(Q/r)² = (Q/4πε₀Ñ)Q/r² = ... = (Q/4πε₀rÑ)Q/r ¦ b = 4πrÑ ¦ or ¦ 4πÑ »depending on application» ; ..

br = 4πrÑ ¦ for the angular momentum deduction — the regular (Kepler) Planck energy E = hf = mcr f = mc² application,

or (in any case: the electric force F is conserved)

b = 4πÑ ¦ for the linear momentum deduction, the mechanical linear momentum p = mv form

Ñ =1 for all stable nuclei ¦.b-max = 8π = 25.13274123;

ElectricForceLaw: pApplication

ApplicationP63

Related physics and mathematics:

The high news breaking point: This is the arrangement — in the following (1S · 1V/M), necessary matching physical units — we must make as (to secure) a separation between stable and unstable — radioactive — nuclei. So: No way this Ñ <>1 arrangement will apply to a stable atom Ñ=1 (not even the most unsharp intellectual focus can miss that one: no way).

Consequence (every single student will finally understand The Basics of and in Mathematical Radioactive Mathematics, I am positive on that one):

— The moment the unstable splits and (eventually) becomes a stable, the differentiation threshold vanishes (by at least two split nuclear components).

bCo: ElectricForceLaw

tIntegral ¦ tHproof ¦ bKOFF ¦ Application P78

In a stable nuclide (Coulomb law) Ñ = 1.0000000000000000000000 ..

F = (1/4πε₀Ñ)(Q/r)² = (Q/4πε₀Ñ)Q/r² = (Q/4π[D/Ξ]Ñ)Q/r²

the electric constant (epsilon ε) factor associated (»N-tilde», Alt+0209) Ñ coefficient = 1, or can so be understood to render such a status, for further testing of the equivalents math-physics basic unit equivalents.

In an unstable nuclide — Ñ <>1 given the equivalent Ñ = ç/c(z) — the numerical Ñ coefficient can have its extreme in

Ñ(MAX) = (ç=c₀)/[c(z)=c₀/2] = 2 (suggesting a max dissonant long lifetime, »LowQ»), and a minimum value of

Ñ(MIN) = (ç=0)/[c(z)=c₀/2] = 0 suggesting a max dissonant short lifetime, »HighQ», (fast dissolving, highly unstable)

The b-coefficient (bcz)

b = 4πÑ ¦ Ñ = 1 for all stable atoms

We designate the numerical 4πÑ as the numerical b-coefficient — testing a related math-physics structural explanation to (nuclear) radioactivity, and its details. For stable nuclei Ñ =1, unstable nuclei ±Ñmax = 2.

The b coefficient can be related directly to Q through the F-form as follows, continued from the above F-rank:

Fr = (Q/4πÑ)Q/rε₀ ; Energy, Joule

(Q) = (Q/4πÑ)        ; partly numerically Ñ-reformulated Q:

b = 4㥠;

(Q) = (Q/b) ; b(Q) = Q unstable radioactive nuclei

b(Q) = Q ;

b(Q)/p = Q/p ;

b(Q)/p = 4πÑ(Q)/p ; Q = Z(e = 1.602 t19 C)

= 4πÑeZ/p ;

The bQp form: ; 1S · U/d bQ/mv = UbQ/mv(d/t) = bENERGY/ENERGY = unitNumerical ;

• 1S · 1V/M · b(Q)/p = 1S · 1V/M · 4πÑeZ/p ; adjusting physical units for comparison:

SimpleEnergy: bCo

——————————————————————

E = UQ ; F = (1/4πε₀Ñ)(Q/r)² = (Q/4πε₀Ñ)Q/r² = (Q/4π[D/Ξ]Ñ)Q/r² ¦ b = 4πÑ ¦ PB ¦ bcz

J = mvr ;

——————————————————————

The simple Energy form: ; 1S · UQ/(mad · t) = 1S · E/Et = unitNumerical ; J=mK=mvr, K Kepler momentum

• 1S · E/J = 1S · UQ/mvr ; J, angular momentum, = mvr (»general mechanic Planck constant equation» [v=c]);

= 1S · 1V/M · Q/mv ; E, energy (J = Et, angular momentum; E = J · f [Planck energy E = hf = h/t; h = Et]);

-----------------

J = angular momentum = mvr

(Planck constant h = mcr = TheNeutron = 1.0086652u · 2.99792458 T8 M/S · [r=1.32 Fermi] = 6.62559 t34 JS)

u = m[6C12]/12 = 1.66033 t27 KG

-----------------

SAMEXRAM ¦

StableUnstable ¦ SchemIllustr ¦ NuclearInstability ¦ bCoefficient ¦ JApplication ¦ pApplication ¦ ElectricForceLaw ¦ bCo ¦ SimpleEnergy ¦

NKCexplain: NKC ¦

TNED related details only

PRINCIPAL PROVISIONS FOR TNED RADIOACTIVITY EXPLANATION

NEUTRINO KEY CODES (NKC)

General designation by the term (γ) Gamma in TNED for all wavelengths from gamma and down

(See: TNED nuclear- NeutrinoSPECTRUM)

NOTE — TNED related physics only — the Planck ring fractal conditions — never approached in MAC:

• there is (Application 74) a Heisenberg uncertainty principle (E = hf = h/n · nf) for every (n:th) fractal level (NeutronDetails) in the nuclear web,

• not only the highest: the experimental visible.

Conditions (»probability statistics» included):

1. The more collected radio nuclides in the same sample, the higher the (mutual) neutrino emissions,

• and The Faster The Count to the abrupt moment of fission:

• The Counting Rate decreases with decreasing left radio nuclides, following the fractal/logarithmic linear tH divisions;

(alike the Cinema emptying on individuals through the entrance: first fastest [short î], last longest)

• The last left radionuclide will have the longest counting time till nuclear split.

• neutrino key code (NKC) enlarges (develops »more data entries to be counted through») in time proportional to the decreased counting rate of dropping off radioactive nuclides.

THE MUTUAL INFLUENCE OF THE AMOUNT of radioactive nuclides resembles that of a Physics Pressure:

Many collected, high pressure (short KEY counting time: NeutrinoKEY unlocks fast — pointing at only the highest intensity focused [the probability condition], one at a time, as the remaining amount decreases), few remaining, low pressure (long KEY counting time).

Explain:

The function that explains the behavior (Resistance× Energy):

U²t = constant RE = R(UQ) ; Ut = R(Q) ; U = constant = R(Q/t = i) = Ri :

• increasing (amount AZ-RAA [»sublime neutrino radiation»] influence on each RAA) Q MEANS:

• increasing i = decreasing R ; (parallel coupling — high mutual neutrino influence)

(the mutual E1818 fractal hf neutrino influence has no affection on the Alpha fission energy, only on the moment of its ejection)

(Many remaining RAA:s means higher rate radio activity, low mean-life; Last RAA lowest rate, longest life time).

(Without this sublime neutrino emitting work energy emissions from RAA:s, this TNED explanation cannot be related).

AZ, mass number (A) and atomic number (Z) family;

RA, Radio Active

RAA, Radio Active Atom

R, maximum resistance to immediate change;

Q, charge — mutually influential (See the bCoefficient) between all AZ-RAA:s in a RA sample;

— All RAA:s emit »sublime neutrino energy» (NucRanks ¦ NeutrinoKEYS) during their RA period;

— The emitted energy relates to each AZ-RAA:s nuclear charge (q) — so that each RAA receives a Q-related (dissociating neutrino, E1818) influence from all the others;

Schematic resemblance functional description

• With (influential) Q per (constant RAA time) t, The RAA constant U regulates a lower individual R on expense of the Q-contributions from all the others;

• U = constant = R(Q/t = i) = Ri: more contributing Q:s means higher current (i), meaning lower R;

• The innate NKC counts faster the more collected AZ-RAA in the same RA sample.

— Reversed:

• the higher number of splitting, dropping off RAA:s from the sample, the lower the count rate (R increases towards its single ideal state), and the longer the (mean) lifetime for the remaining before splitting.

• Each ideally isolated AZ-RAA has one and the same fixed maxR working on an internal AZ-RAA constant voltage U — it is an AZ-RAA property:

The constant U (associates the actual radio activity OF the atom) defines the property of an unstable atomic nucleus/atom:

Stable atoms (U=0=R) have no connection to these specific mathematics

(U=0, R=0: a stable atom has no losses, needs no refill to continue on its natural intrinsic spin).

(A RAA must use innate produced WORK = energy from its own mass [as in a neutron decay] during its RA period in order to [structurally] rebuild itself for the future coming split).

THE R FUNCTION:

NKC: NKCexplain

(NKC) NEUTRINO KEY CODE (LENGTH x = 1/√3 = power top on the energy function),

• count is highest, shortest lifetimes, when each RAA is surrounded by many alike, lowest (longest count) when standing all alone:

— Situation Beginning from the individual (R), when its starting lifetime before splitting is shortened — in proportion to the amount of others alike around:

— The first AZ-RAA to split and leave the RAA sample will have the shortest lifetime of all.

• As the number of AZ-RAAS drops of, the remaining lifetime of the next to pass out will be slightly longer .. to the end with the remaining single longest (greatest) R.

— The single R (resistive) RAA property works so to be reduced by the (neutrino influence emissions) amount from the sum of the surrounding alike.

• The »mutual neutrino» FOCUS in the sample where an AZ-RAA-nucleus splits and leaves the sample, is so (self auto regulated) dynamically determined — not static:

— (reducing R-) FOCUS SHIFTS DYNAMICALLY: »the Next To Split Spotlight» always falls (least resistance principle) on that AZ-RAA which has the momentarily fastest (least resistance count) NKC, the one about to drop off next:

• temperature and atomic lattice bounds, determine (to some extent: probability statistics) which actual AZ RAA-atom shall be the first .. second .. third .. and at last .. to leave the sample.

• However as ideally mathematically exact the overall definition of the logarithmic decay is presented, there is a corresponding EXACT timing for each dropping off AZ-nucleus.

(BUT EXACTLY WHERE IN THE SAMPLE THAT NUCLEUS IS POSITIONED IS A MORE PROBLEMATIC QUEST TO ANSWER: it is dynamically [»statistics»] determined).

Without the Planck Structural Constant equivalent

[h=mcr= (n→∞)[m/(n→∞)] c [r/(n→∞)](n→∞)] — a fractal concept — these related details cannot be explained, nor understood.

HOLLOW TOROIDAL FRACTAL RINGS

PLANCK RING STRUCTURAL CONSTANT

h = mcr = 1,0086652u · 2,99792458 T8 M/S × 1.32 t15 M = 6,62559 t34 JS THE NEUTRON :

m = [n→∞](m/[n→∞]) = m ;

• The atomic nucleus is a fractal, TNED says.

• With innumerable structural (neutrino — infinitely high frequency, small energy) levels:

E = hf = mcr f = mc (r/[n→∞]) · [n→∞]f = E

Unstable nuclei (RADIO nuclei)

• are born with an excess (to be wasted — very small mass destruction [m→γ]) energy — scanning the nuclear entire structural building (emitting sublime neutrino (»high gamma») Planck structural energy due to the work needed to rebuild the nucleus and prepare its coming splitting — aspiring to a stable end condition with zero innate mass destruction):

IT TAKES TIME to scan the nuclear level structures (NeutroDetails ¦ RamBam):

• Each (Alpha radioactive) atomic family (AZ) has its own specific NEUTRINO KEY CODE (NKC) — a Type n! encryption that must be Counted Out/Through before Marker Reached.

• The NKC time equation relates to

1. The ENERGY associated with the emission of the Alpha (2He4) nucleus — effectively reckoned by subtracting the Alpha and Daughter atomic masses from the Mother atomic —

defines the effective atomic mass energy defect of that AZ family;

This energy (i.e. its power top derivative) level where the mother radioactive atom splits into two (Daughter + Alpha), is (ideally, just mass difference) exactly the same for all same AZ

• but the occasion of the splitting moment is a (conv. probability statistical [logarithmic]) function based on the AZ half-life (tH=t½) constant;

Relating

2. the number of seconds in t½=tH=half-life for the AZ family, multiplied with the AZ-nuclear number of »NuclearTurnTransmissions» per second (roughly averaged for all radioactive AZ atoms T20 = 10^20 per second):

• Each turn can be designated an AZ ”click” where the idealized nuclear spin has rendered one complete nuclear throughput of its most fundamental rebuilding aspect [A (»small contribution») DeltaWork nuclear structural parameter],

• craving a (very) high number of such (level structural) turns, in order to complete the NKC »coding» to its last digit (n);

— The higher number of present AZ atoms in a sample, the faster the counting, due to the higher mutual neutrino influencing pressure (as TNED-suggested):

• The atoms’ thermal vibrations and their different locations in the sample, all changing dynamics, never a stable static condition, will (probability statistics) secure that only One At A Time most focused AZ by the other atomic nucleus will split;

(»never two or more» at the same occasion ..).

• When that AZ atom has left the radioactive AZ sample, the remaining sample’s total neutrino pressure/activity has decreased. And the following dropping off atom will (n!) count on a lower rate, securing an ideal lengthening lifetime before another each successive splitting AZ — leaving the last radioactive AZ atom to have the longest slowest NKC time:

NKCexplain ¦ NKC

RadioMathAug2026: — ¦ StabUnstab ¦ Graphs ¦ Rfunction ¦

Inte förrän nu (Apr2026) i AfterMath har en helt tillfredsställande — komplett — förklaring enligt TNED visat sig:

Framställningen i TNED från Jul2017 (och föregående) blir ett arkiv för hur hela upplösningen kom till (nu Apr2026).

TNED-fysikens olika avsnitt redovisar helt andra förutsättningar än vad populationerna inom MAC är förtrogna med för att tackla problemdetaljerna. De avgörande punkterna finns, som sagt, inte representerade i den nuvarande akademins litteratur.

StabUnstab: Graphs: RadioMathAug2026

Author’sREF: Graph Functions TNED110.BMP ..

RadioBirth ¦ RadioBase — The Energy Integral ¦ E1818 ¦

Preferences Stable-Unstable in PREFIXxSIN:

STABLE:

———————————————————————————————————

— Horizontal x-axis (or X-plane): ± unlimited extension with no deviation;

EXAMPLE y=0, x=x.

UNSTABLE:

EXAMPLE: y = sinx^3, x in radians,

— Any f(x) wave function >0 with ±x as the variable and ±y as the resulting amplitude:

is a UNIT (x;y)=1 frequency modulated wave form beginning at amplitude y=1 at its longest wave period, then further with decreasing wave periods through the sine x values alternating between ±1 as x→∞.

Application (US: unstable-stable) — from Stable to Unstable:

— All stable atomic nuclei is characterized by no change: no disintegration, no fragmentation, perpetually exposing their physical properties without need of refueling

(meaning that the sum of moments and forces in the stable atom is a net zero: the stable atom experiences no losses due to its factual electro-mechanical existence).

(We imply no ionization processes, type Solar Planck energy irradiation on the Earth top atmosphere, generating the Ozone shield layer from water molecule dissociation with some accompanying Hydrogen escape to outer space).

EquationStable:

y = 0. Stable nuclear/atomic conditions:

————————————————————————————— ..

EquationUnstable:

±y>0, x=±y; y = (0.1x)(sinx^3);

Same equation as the previous. Only difference (the ± 0.1x tangent ±y extension) is that the wave amplitude begins from zero (»no immediate change»), then growing (corresponding additional Intensity) in amplitude as the frequency increases (illustrating PSCE [Planck Structural Constant Energy, E=hf] an inner STRUCTURAL nuclear separation process, about to cause »a future burst» that will separate the 92U238 from the coming 90Th234 by »the amplitude band 2H4 at some significant future point»).

— The x=0 point situation should (perfectly) illustrate the (ideal) situation where a radioactive (alpha) nuclide is born — for example the 92U238:

• From birth (x=0), the 92U238 nucleus does not decay immediately, only by TIME (unequivocally through extension of +x-values on a PSCE premise);

• The unstable condition entails an inner ongoing (very sublime: what we know, no directly spotted emitted hf-quanta) PROCESS (like a Pregnancy) awaiting The Opportune Moment when The decay (Alpha particle) is launched and the 92U238 becomes split to a couple 90Th234 + 2H4.

NUCLEAR EXAMPLE

In Polar coordinates

the math form is explaining strikingly exact:

The unstable nuclide, from birth (made from a fusion from lower lighter nuclei) begins directly from the deepest fractal levels, working itself up to »Surge Mode» (illustrated by decreasing frequency and amplitude intensity: »the moment of birth»: release)

• until the nucleus breaks apart on the actual splitting moment.

NOTE the Planck ring fractal conditions — never approached in MAC:

• there is (Application P74) a Heisenberg uncertainty principle (E = hf = h/n · nf) for every (n:th) fractal level (NeutronDetails) in the nuclear web,

• not only the highest: the experimental visible.

— TNED only, not MAC, can discuss »infinitely high nuclear related frequencies» — on infinitely low energy, because of this basic principle fractal provision.

Breaking Property

— Alpha particle ejection. Nuclear spontaneous fission.

90Th234 + 2He4 = 92U238

92U238 – 2He4 – (m→γ) = 90Th234 ; (m→γ) = 92U238 – 2He4 – 90Th234;

The most relevant (TNED) interpretation:

Beginning from the highest frequencies (Compton [fractal] effect) the unstable mother nucleus performs WORK (m→γ) until the moment of a sudden sharp breakthrough where (typically) an Alpha (2He4) nucleus is ejected — and the mother nucleus becomes perfectly stable.

— The short (shortest) wave part in the illustration (upper +x axis) represents the triggering moment where (pacing down ..)

• 1. The unstable nucleus is born (from lower nuclei fusions)

• 2. on an already (so) determined (b-coefficient) dissociative (inner fractal nuclear unstable resonances) energy which the unstable nucleus must generate from its own mass (m→γ) during its »pregnancy period» until

• 3. the moment of (Alpha) fission.

In principle, this Alpha particle emission energy (atomic mass difference »calculated internally by the RAA») is already determined — cannot change — from the RAA:s moment of birth.

— INFLUENCE (the unstable work m→γ) emitted from the same family (RAA) radioactive atoms (»highly specific Neutrino Keys» for each radioactive family type, the b-coefficient: nuclear charge RAA instability), contributes to speeding up the mother nuclear vibrating state, leading to the 2He4 ejection.

— The more RAA dropping off, becoming stable, the less the common influence. And the longer »the pregnancy period» of the (last) about to decay mother nucleus.

— While the Alpha particle ejecting energy is (practically) the same for all those Nuclear Family ejections, the occasion when it happens (individual half life) extends significantly as the number of RAA drops off becoming stable.

Further details below illustrates the principle function (says TNED).

Rfunction: StabUnstab

Schematic — energy, power, power max (breakthrough):

Calculated illustration’s solution

ENERGY:

y = ½[1 – 1/(1+x²)] + ½[1 – 1/(1+x²)]

= (1/2)[2 – 2/(1+x²)]

= (1/n)[n – n/(1+x²)]

= n(1/n)[1 – 1/(1+x²)]

= E = hf = mcr f = mc(r/n) · n(f), n:= n→∞, x = time;

Energy J;

1–(1+x'2)'–1 ;

derivation:

Dn = –(–1)(1+x'2)'–2 · (0 + 2 · x^1)

= 2x(1+x'2)'–2

Power W

Dn AB = A’ B + AB’ ;

A’ B = 2(1+x'2)'–2 ;

AB’ = 2x[(1+x'2)'–2]’ = 2x[–2(1+x'2)'–3 · 2x]

= –8x²(1+x'2)'–3 ;

Dn AB = A’ B + AB’ ;

= 2(1+x'2)'–2 + –8x²(1+x'2)'–3

= 0 ;

Power curve top value:

8x²(1+x'2)'–3 = 2(1+x'2)'–2 ;

4x²(1+x'2)'–3 = (1+x'2)'–2 ;

4x² = [(1+x'2)'–2]/(1+x'2)'–3 ;

= 1+x² ;

4 = 1/x² + 1 ;

3 = 1/x² ;

x = 1/√3 ;

= 0.577350269.. ;

The unstable condition develops to a point where a strong surge breakthrough is launched.

THE CONDITION

begins from the moment of the unstable nuclide’s birth: the deepest possible fractal levels (highest possible neutrino frequency, on its lowest possible energy: E’’ = hf = h/∞ · f∞ = hf = E’’)

(from a previous fusion occurrence, or from the moment where a further unstable component appears from an actual fission).

The amplitude INTENSITY-feature continues and develops (on wavelength: the remaining RAA:s influence) until the dissociation energy marker level has been completed reached, and the nuclide quickly splits during a (t20 S: taken approximated on a 1 turn nuclear c-spin) short moment.

Larger amount remaining RAA:s means that the end finishing total amplitude rises faster: Marker Reached comes sooner : Shorter mean life for the nearest coming decaying nuclide. The last decaying nuclide will have the longest mean life time. And its amplitude intensity on the breakthrough threshold will (so) be the lowest (The RAA:s own individual default on its Z-family conditions).

— With this explanation, there really is no room for ”statistics” or ”probability” in understanding the main (ideal) process.

Rectangular coordinates

GRAPH: y = 0+0.066x[(1.2sinx'3)–1.2]

92U238 – 2He4 – (m→γ) = 90Th234 ; (m→γ) = 92U238 – 2He4 – 90Th234;

Nuclide unstable (internal resonant neutrino ripple) Amplitude/frequency (A/F) begins at the Highest frequencies on the deepest fractal levels. Then approaching a finalization towards zero where the (2He4 Alpha) fission quickly ends the process.

The One Hundred Billion Question:

What determines the »Marker Reached» decay energy — when the 2He4 is ejected?

TestAnswer:

— When an unstable nuclide is produced (from exothermal fusion), each such atomic family is given its own specific unique (inside structural neutrino-) KEY (NKC):

• That KEY defines a specific (radio active) b-coefficient — which can only be determined by knowing the actual decay energy (MeV) and the actual half-life (tH) of that atomic unstable family. What we know (today): that specific KEY b-coefficient cannot be directly calculated, however be defined to its limits covering all the unique KEY features for each radioactive decay family of atoms.

AS ALREADY HAS BEEN OBSERVED (ideal math conditions):

Radiomath explained — same math as in Wikipedia, but here »slightly further enhanced in clarity» (the underlying implied dynamic explanation):

FREQUENCY: »inner nuclear business»: every radio active nuclide has its own (»neutrino») Key; unique for that atom only (structural criteria).

— The bandwidth (±Amplitude) determines the »structural depth» as the process continues (Compton effect: always from higher to lower frequencies) till Alpha ejection.

AMPLITUDE: intensity parameter: The more collected radio nuclides in a given sample, the higher the collected mutually dependent Amplitude (and the faster the splitting moment for the nearest next RAA to divide: last RAA takes longest time):

• Large initial (N0) quantities generates the first decaying nuclide on a short mean life interval:

• As the sample looses radio nuclides, the N0 condition Amplitude summing decreases, and the next (second) decaying radionuclide receives a slightly longer mean life interval:

• The last nuclide to eject an Alpha particle will have the longest possible Amplitude decreasing period until the splitting 0 time, and longest possible mean life interval (t = N0 · tH).

RADIOACTIVIY ARTICLE END.

RadioMathAug2026 ¦ StabUnstab ¦ Graphs ¦ Rfunction ¦

bHspectrumOrigin: — TNED details From Nov2007

E1818 ¦ NucRanks ¦ bcz ¦ bCalc ¦ bPrevious2017 ¦ bStatus2026 ¦ AlphaChan2017 ¦ bDeveloped ¦ Radio2017 ¦ GeigerForm ¦ RadioRelatedMAC ¦ RadioRelatedTNED ¦ InfectedTerminology ¦

From the 2007 TNED edition of Spectrum and Quantum Numbers

Original observations in H-spectrum

bCo

Nukleära kapacitivitetsfaktorn Ñ

Praktisk, säker Exempelreferens från Vätets Spektrum:

— I Spektrum fick vi till jämförelse [Se Väteatomens grundradie] den motsvarande DIVERGENSEN v=ξ/n [ξ, xsi] enligt 2,1875325 T6 M/S eller v/c(0)=0,00729682, eller avrundat 7/1000 av c(0).

— Den praktiken visar att en teori för en »nukleär kapacitivitet» [Ñ] kan antas — för vidare prövning — här, endast, med stöd i ovannämnda tillämpbarhet på elektronmassans komponenter, och därigenom via neutronsönderfallet en motsvarande PRINCIPIELL förankring i atomkärnan, och endast så;

— Kärnomvandlingar enligt TNED innefattar i vilket fall POTENTIALBARRIÄREN med ALLA inre möjliga omsättningar av atomkärnans centralmassiv ±A909e (1818-massivet, neutronen: mn/me = 1818+18+2,624); Kärnan avgör själv, från fall till fall, vad som gäller. Och det är (således) här en helt meningslös uppgift att försöka reda ut »alla möjliga fall» genom »en enhetlig ekvation». Vi behöver [därför] endast koncentrera oss på de enklaste grundsambanden ..

E1818:

RadioBase

Sambandsformerna i TNED (NeutronBasics)

för beta- och alfasönderfall:

TNED-fysikens två centrala led

i ämnet instabila atomer (betasönderfall eller direkta kärnsönderfall)

— elementärt enkla matematiskt balanserande utskrivna kärnreaktionsled:

NucRanks: E1818

ATOMKÄRNANS RADIOAKTIVITET

———————————————

Nuklidkoefficienten b med U238 ¦ Betasönderfall och nuklidsönderfall ¦ Radioaktiva sönderfallet i relaterad fysik

Förenklat (nu Apr2026) — med tilläggen +E’ och +E’’

och förtydligat fullständigt för nuklidsönderfallen:

— NEUTRINOINFLUENSER (+E’=hf[1818]) FINNS HELA TIDEN mer eller mindre — som mest i himlakroppsbildningens primära skede, +E’): det blir helt omöjligt att utesluta. Sedan kontinuerligt (+E’’) med ömsesidiga influenser beroende på storlek och omfattning — som knappast ens kan mätas instrumentellt på grund av den ringa influensen

Alfasönderfallens radionuklider

– E =hf[1818] ordinära dissociationsenergin som definierar radio AKTIVITETEN. Finns inte den, är nukliden stabil;

+E’ =hf[1818] lokalt exotermiskt tillskott — kan bara ges från Dmax atombildningarnas primära skede (nukleära strålningstryckets matematiska fysik)

+E’’=hf[1818] marginella ömsesidiga influenser, gäller inbördes i alla radioaktiva lokaler:;

— Inverkan från den sistnämnda E’’ är principiell — men vad vi vet helt omöjlig att kunna mäta på grund av neutrinokaraktären i E=hf[1818] och dess ytterst låga energitäthet sedan väl Dmax atombildningarna slutförts.

Relaterad fysik och matematik

Hela den radioaktiva matematikens (härledande) förklaring bygger (här) helt och hållet på sambanden som kopplar potentialbarriärens energizon —

(stället — energizonen c = c0/2 = cz — där den elektriska laddningen TAS, den ideala grundmatematiken: Applikation76¦78)

kriteriet för atomkärnans perfekta balans och stabilitet: grundmatematiken till begreppet ytladdningstäthet

(surface charge density Q/A = D).

— Potentialbarriärens grundfysik och matematik finns inte omnämnd i moderna korridorer. Se Applikation63 (QImath).

— Vi kunde inte, meningsfullt, visa hur radioaktivitetens (härledande) fysik fungerar utan att först ha viktiggjort potentialbarriärens härledande, avgörande, innehåll. I moderna korridorer kompenseras den detaljen av sannolikhet och statistisk matematik. Med härledningarna här blir den delen helt överflödig (b-koefficienten) — säger TNED. Hela komplexet kan förklaras i varje detalj.

bcz: NucRanks

See PotentialBarrier REFERENCES.;

tIntegral ¦ tHproof ¦ bKOFF ¦ Application P78

Related physics RADIOACTIVITY MATH BASICS

Nuclear surface charge density stability, TNED applications

Application P78

(Nuclear) Charge density D= Q/A ¦ Ñ = ±ç/cz = ±(çMAX=±c0)/(c0/2) = max±2; (Ñ=1) = (ç=cz);

ç (»c-comma» [”cCOMA”, Alt+0231 ASCII]) connects and relates Spectral (frequency variation) details

(orig. from H-spectrum math).

Light’s Gravitational Dependency included — Application 75;

b-coefficient: 4㥠in the electric force law:

Electric Force Fundamentals (Coulomb law):

F = (1/4πε₀Ñ)(Q/r)² = (Q/4πε₀Ñ)Q/r² = ... = (Q/4πε₀rÑ)Q/r ¦ b = 4πrÑ ¦ or ¦ 4πÑ »depending on application» ; ..

b = 4πrÑ ¦ for the angular momentum deduction — the regular Planck energy E = hf = mcr f = mc² application,

or (in any case the electric force F is conserved)

b = 4πÑ ¦ for the linear momentum deduction, the mechanical linear momentum p = mv form

Ñ=1 for all stable nuclei:

————————————

— D = Q/A, »surface» charge density:

— A stable nuclide exposes no surface (TNED charge) fluctuation.

— A radioactive nuclide does (or must so do, in order to offer an explaining triggering physical property of type instability: nuclear TNED only surface wave form fluctuations, one way or the other).

• Beginning from the deepest possible nuclear fractals, the decay process develops

• by performing inner nuclear rebuilding (neutrino level, E1818) work (m→γ)

(RadioBasics ¦ RanBam ¦ StabUnstab)

• until Marker Reached, and the nuclide splits (reaching a stable condition).

• The b-coefficient (»nuclear capacitivity») reflects a guide of the nuclear characteristic and its (TNED nuclear surface) charge status.

BeskrivningÑ: (From HydrogenSPECTRUM, TNED related physics and mathematics only)

b =4πÑ ¦ Ñ = ±ç/cz = ±(ç=c0/2)/(c0/2) = max±2; bMAX = ±8π ± 25.13274123

bQ/p = 4πÑQ/p ;

p, F/A pressure (influence) related physics (nuclear charge ripple variations on unstable nuclei)

Ñ = 1 FOR ALL STABLE NUCLEI

for all stable nuclei:

• Max Ñ (»n-tilde», ASCII Alt+0209) = ±2 (antimatter included):

— we study that in The Potential Barrier (Application 75, Application 78) basic math, and see how it works by detail.

(The b=8π features significant Alpha energy expositions, explaining earlier not known details: collecting all experimentally tabled alpha energies by offsetting one and the same b-curvature).

bCalc: bcz

ALPHA RADIOACTIVITY; radio nuclide charge Z known (also Alpha particle mass m known), the Alpha particle energy E and its atomic family typical half life (tH) must be measured to find that family’s typical b (»nuclear charge capacitivity»):

b = (√2mE/Ze)ln(t_H/1Sln2)

b cannot (what we know at the present) be calculated directly;

(TNED involves Dmax aspects when atoms first are formed in our universe [K-cell Heat Physics], also forming their future history: b becomes »a primary baked» property [so we cannot calculate it .. what we know .. at the present ..])

b can only be determined through knowing the (Alpha releasing) energy E, the nuclear charge Z, and the half-life (tH) of that specific atomic family.

MAC — must use statistics to relate radiomath:

E = hf = mc² — water drop nucleus model; no extensive structural significant morphology.

MAC nuclear Radioactivity: statistics and probability (Gamow 1928).

TNED — uses the b-factor with Planck constant = Neutron nuclear fractal facilities to explain:

E = hf = mcr · f = mc(r/n) · (n)f — n approaches infinity; Planck structural constant fractal toroid.

TNED nuclear Radioactivity: structural nuclear (neutrino) radiation pressure (p): k = A0/2tH:

(neutrino influential processes with not [at present] detectable low energy levels);

the more radio individuals leaving (decaying out of) the sample (N0)

the less common nuclear radiation pressure.

MEANING:

the longer extending individual radionuclide lifetime:

The (p) pressure reduction defines the remaining radionuclide lifetimes. Not statistics.

The MAC principle Geiger-Nuttal formula is the same in TNED, with a small addition (b-coefficient)

• explaining the nuclide significant property versus half time and alpha nuclear decay energy.

TNED:

The nuclear radioactive atom is produced as an

(from an exothermal Dmax fusion — with a net resulting small mass deficiency which defines the actual instable condition)

• unstable — vibrating, emitting sublime mass to neutrino (E=hf) radiative — nucleus

• until an alpha particle is emitted (or the nucleus is split, or until),

• and a nuclear stable condition is established.

— Additional (near) radio nuclei (dissociation neutrino emissions) contribute to a general higher (h/n nf neutrino energy) pressure, promoting shorter (higher dissociative energy INTENSITY) individual radio decaying lifetime.

• The formulae (8.1) is already well known.

• As the (SITE) nuclear radiation pressure decreases with reduced radio individuals in the sample region, also their decaying lifetime approaches (increases) a final that of a single one alone radionuclide.

No need for statistics and probabilities. Simple (nuclear radiation pressure influence) pressure math — apparently unknown in modern quarters: no TNED physics.

TNED physics has no statistics. Never used in Universe History.

bPrevious2017: bCalc

b-koefficienten, radioaktiva sönderfallets matematiska fysik

I SAMBAND MED (Jul2017) UPPMÄRKSAMMANDENA HÄR (Apr2026) GJORDES EN ALTERNATIV TOLKNING AV FÖREGÅENDE (Jul2017) BESKRIVNINGAR AV b-koefficientens radiometriska kopplingar.

— Vad var det som tillkom .. och gjorde att »en alternativ Lösning» infann sig .. ?

• b-koefficienten, dess redan genomförda härledning, tolkning som

(och åt vilket HÅLL man relaterar begreppet »energigenomströmning» .. inte riktigt väldefinierat då Jul2027)

• en fast alfa radioaktiv nuklid relaterad massrelaterad KONSTANT.

Den delen kom aldrig fram från början (2017).

b is not affected by the nuclear life time variable intensity at site:

— What MIGHT be affected is the E (alpha) energy part — but with so small deviations that it is practically impossible to prove by direct experimental observation, what we know.

bStatus2026: bPrevious2017

The general (TNED Aug2026) picture is that E and tH are proportional (for any sample Z-related collection of radio nuclides)

Proof:

Atomic masses: U1– U2 – U[2He4] = Effective DecayEnergy.

The mother nucleus emission of the Alpha particle (the fission) energy is practically one and the same. But the moment where it happens has general influential (»statistical») provisions.

b = (√2mE/eZ)ln(t_H/1Sln2)

alla enheter i internationella MKSA systemet: Meter Kilogram (KG [»Gram = mK, milli K»]) Sekund Ampere

Knowing the Alpha particle physics (m, Z) the half-life (tH) and the Alpha energy (E)

— its effective energy is just frankly, by example:

[m(92U238) – m(90Th234) – m(2He4)] · c²/([e=1.602 t19 C] · 1T6) in MeV

AlphaChan2017: bStatus2026

The mass difference of the components (which, compared to Alpha Channel measures deviates just slightly. See ARI: General TNED b-coefficient calculated Radio Isotopic Picture, 2017).

— The b-coefficient as such can be calculated from these — and so tabled for each atomic (Alpha decaying) family: This gives a (simplified) picture of the (Alpha) radioactive mathematics — however on a form that cannot be deduced in modern corridors (The bCoefficient). The TNED atomic nuclear details: all Planck Ring mathematics.

t_H = 1Sln2e^beZ/√2mE

ln[t_H/(1Sln2)] = beZ/√2mE

e 1,602 t19 C

Z atomnummer (= 2 för Alfapartikeln 2He4)

m alfapartikeln massa: 4,0026031 · 1,66033 t27 KG

E alfapartikelns uppmätta rörelseenergi vid sönderfallet,

tH medelmässigt uppmätta sönderfallets halveringstid,

1S en sekund

b för U238 på första alfautkastningen (4,267 MeV) är 11.8592680796

bDeveloped: AlphaChan2017

— I framställningen Jul2017 betraktades b-koefficienten som en VARIABEL

• i omgivningar med hög energitäthet (primära himlakroppsbildningarna).

Med (i princip) konstant utkastningsenergi för alfasönderfallets 2He4 kärna (4,267 MeV i U238 fallet)

• togs (Jul2017) omgivande exotermiskt avgivna E=hf[1818] Planckenergier (primära himlakroppsbildningarna) som ändringsagenter för b-koefficienten (Jul2017):

• högre b-värden (»högre energigenomströmningar»), större e-potensvärde,

• betyder längre halveringstider (tH)

Funktion (Apr2026 först) (NucRanks):

FULLSTÄNDIG FÖRKLARING

OM b-KOEFFICIENTEN ISTÄLLET relateras som en fast specifik radionuklids massrelaterade parameter

• eftersom i vilket fall, primära exotermiska fusionsbildningarna,

• alla radioaktiva atomer/kärnor bildas just radioaktiva

• oberoende av omgivningen,

och istället (särskilt via himlakropparnas primärbildning: enorma exotermiska energier avges, se nedan exemplet med bildningen av Järnkärnan för Jordens del) omgivningens olika möjliga

• den radioaktiva dissonansenergins –E=hf[1818] MOTVERKAN

• +E’ tas som hämmande –E utfallet (–E definierar radionuklidens radioaktiva status, till skillnad från en STABIL atom där –E = 0: radionukliden genomlever interna vibrationer vars arbete tas från den nuklidens egenmassa, dissociationsenergi, TILLS ett utbrotts sker, och en alfapartikel kastas ut)

uppnås precis samma nettoeffekt med en högre e-potens — b intakt:

• Nettoverkan på normala (uppmätt i ett redan atomutvecklat universum) alfapartikelns utkastningsenergi, blir med signifikanta +E’-tillskott LÄGRE, som

• ger ett högre e-potensvärde, och därmed längre tH.

— Vartefter universum (expansion) utvecklas, avklingar +E’ tillskottet — och i ett full utvecklat (flera, många) miljarder år senare universum, gäller bara i princip normaltillståndets b-form med +E’ = 0.

• Återstår ett möjligt (helt försumbart) +E’’ som KAN påverka — men knappast uppmätas

• EFTERSOM de neutrinoassocierade frekvensernas energier ligger helt utanför mätutrustningarnas möjliga upplösning:

• variationer finns alltid — men i statistiska räkningar på givna mätobjekt, raderas alla olikheter, och endast ett genomsnittligt mätvärde framträder.

— Vilket också i princip (»men omöjligt att mäta») med variationer i Neutrinostrålningen från Solen — olika Jord-Sol avstånd, Soleruptioner, Solrotationen själv — ger minimala variationer.

• Allt annat vore verkligen underligt: fysiken definierar enbart variabla tillstånd (på givna naturkonstanter).

Radio2017: bDeveloped

GRUNDERNA FRÅN 2017

zrefRF.htm#HärledningenGeigerNuttalTNEDGrund

Härledningen till sambandet för halveringstiden enligt TNED

zrefRF.htm#SönderfallsstyrkanMAC_TNED ¦ zrefRF.htm#Sönderfallsstyrkan

Sambandsform (»tH-universalen» — tHuniversalen) — nuklidformen:

t_H = 1Sln2e^beZ/√2mE

beZ(2mE_J)^–0,5 = b[6,94348949](E_MeV)^–0,5

Sambandsformen ovan, explicit utvecklad i ledet under för Uran 238 sönderfallet, är precis densamma som den traditionellt härledda s.k. Geiger-Nuttalls formel — men här vidare preciserad (se Härledningen 2017) genom TNED-fysikens förutsättningar.

GeigerForm: Radio2017

Geiger-Nuttalls ursprungliga formel

har motsvarande uttryck (via Alfaenergin Eα)

ln2/tH = A · e^–(B/√Eα) = λ ;

ln2/tH = A · e^–(eZ/√Eα) ;

A = ln2/tH · e^(eZ/√Eα) ;

A in (e-power numerical) per half-life Seconds (frequency) ¦ a not very informative parameter .. »inverterad sönderfallsfrekvens»

[Oct2011, eq. (7.54): http://labspace.open.ac.uk/mod/resource/view.php?id=431626]

tH = ln2 · (C=1/A)e^(eZ/√Eα); Eα, AlphaParticleEnergy

MAC-theories. statistics and Tunneling (Basic works from George Gamow around 1930).

TNED: Not even close to.

Sönderfallsstyrkan — halveringstiden — ändras INTE med neutrinovariationer i influenser (särskilt noggranna instrumentmätningar efter Jenkinsgruppens observationer från 2008). — Men TILLFÄLLET för sönderfallet kan skjutas upp (»be put on hold») om motsvarande nukleär Planckrelaterad E=hf sönderfallsenergi (Neutrinoenergi, E[hf(1818)]) påförs ursprungsnukliden vid dess bildningstillfälle — säger ovanstående konsekvensmatematisika Ehf1818 led. Det är en ren TNED härledd bildningsform; √2mE = konstant oberoende.

RadioRelatedMAC: GeigerForm

• Inverkan av det mottryckande +E’ (nukleära strålningstryckets matematiska fysik, ingår inte i moderna kvarter, endast TNED har den härledningen, se vidare SOLFYSIKEN)

• reducerar E-faktorn i √Eα = √2mE — som resulterar i att E-potensen växer — och därmed också tH tillväxer i tid: U238[E=hf(1818)]-sönderfallet fördröjs

• tills U238 tillskottet +E´i tidens längd (många miljarder år krävs) tappas ur och den kvarvarande andelen radionuklider antar det mera normala »+E’ = 0» tillståndet;

— Och det ska här sägas direkt, som räkningarna visar: tillskottet +E’ som krävs för att göra signifikant skillnad i tH värdet i förhållande till det nominella E-värdet

• är bara några få procent (om ens det). Den relativt stora påverkan från ett +E’ — kan endast uppträda under den primära kroppsbildningens allra första Dmax exotermiska fusionsbildande sekunder (liknande GRB-observationerna från de mest avlägsna regionerna i vårt synliga universum) — borgar för att alla efterblivande universaltillstånd INTE nämnvärt förmår påverka halveringstiderna — även om små, praktiskt taget omöjliga att mäta, differenser uppträder: neutrinoinfluensernas oförnekbara påverkan, men också instrumentellt helt omöjliga påvisbarhet på grund av deras höga (nuklid-) frekvenser — och den TID det tar för att påvisa eventuella förekomster (»tusentals år»).

Se särskilt (2008) Observationerna från Jenkinsgruppen (variationer på Jordytan på grund av olika avstånd Solen-Jorden, samt Soleruptioner och Solrotationen självt), som senare (numera) avskrivits på grund av osäkerheten i den ytterst känsliga mätapparaturen (och inslaget av statistisk matematik).

RadioRelatedTNED: RadioRelatedMAC

— b-koefficienten sätts som en massbaserad radiorelaterad Norm-koefficient. Så, nämligen, att: istället för att b ändras med +E’, som är en Planckenergi, inget masstillskott, behåller vi b-värdet och låter istället e-potensens rot-E värde (–E=hf[1818]) reduceras med ett +E’. Det beskriver dynamiken i en mera relaterad form — men som

aldrig kom att associeras till i föregående beskrivning (2017).

SLUTSATSER ENLIGT TNED, Aug2026

När väl universum är utbildat i sina stjärn-, sol- och planetsystem är b-koefficienten den fastlagda som gäller i varje fast mineralogiskt uppmätt form: radioaktiva mätningar;

• b-koefficienten kan då inte ändras för en given radionuklid,

• därför att motsvarande neutrinoenergier från solar och stjärnor i deras E=hf emissioner är så utglesade att de inte längre har någon signifikant betydelse för variationer i halveringstidsvärdet tH (säger TNED). Och det skulle vara hela förklaringen.

(En bilförare i Stockholm försöker Tuta åt en Trafikant i Tokyo ..).

Som det instabila tillståndet fortlöper för den aktuella radionukliden, urtappas Planckenergins tillskott +E’=hf(1818) från det speciella unika (första celesta) exotermiska (Aktivitetens naturliga avtagande med tiden) bildningsögonblickets tillförande. Kvarvarande radionuklider, i takt med urtappet, kommer till slut att enbart använda det egna massbaserade [K] – E=hf(1818) kapitalet (Geiger-Nuttalls formel); Det som enbart kan börja mätas meningsfullt från första tillgängliga fasta mineralogiska (ytjordiska) fasta tillståndets fysik.

InfectedTerminology: RadioRelatedTNED

DEN INFEKTERADE ALFAKANAL TERMINOLOGIN ¦ Webbreferenser — 2011 — det är tydligen det statistiska inslaget som skapar förvirrande EXAKTA besked ..

Alla Radionuklider ¦ Allmänklassifikation ¦ Överblick — sambanden ingår inte i MAC ¦ Nuklidkoefficienten — b ¦

(Hela komplexet i MAC är infekterat fragmenterat på grund av DET STATISTISKA inslaget som slår sönder varje EXAKT — alfasönderfallet explicit med kärnteorin i MAC).

SambandenMAC— källreferenser, citat:

— SÄG (sedan) inte den ENORMA omständlighet som tH-sambandsformen RENDERAR i modern akademisk facklitteratur. Det är sannolikhet, kvantfysikaliska specialbegrepp och snurrande och studsande partiklar i atomkärnan som poppar upp och, garanterat, gör rent hus med publiken. Noll applåder. Det finns inte en själ kvar, ens på ståplats. Man blir så fängslad att man (snart sagt) får betala för att gå UT.

Med TNED-införandet av en nuklidkoefficient (b-koefficienten) framträder en mera begripligt användbar sambandsform

• b (Ñ≠1) blir helt baserad på redan uppmätta tabellerade alfaenergier för de olika radionukliderna, och med vars hjälp (den medelmässiga) tH-faktorn kan bestämmas (med hänsyn till radionuklidens massa ..).

bHspectrumOrigin ¦

E1818 ¦ NucRanks ¦ bcz ¦ bCalc ¦ bPrevious2017 ¦ bStatus2026 ¦ AlphaChan2017 ¦ bDeveloped ¦ Radio2017 ¦ GeigerForm ¦ RadioRelatedMAC ¦ RadioRelatedTNED ¦ InfectedTerminology ¦

bKOFF: RadioAlphaEnergy ¦ RadioBirth ¦ NALRadioTNED ¦ RadioDisclaimer ¦ RadioUnstableNature ¦

TNED related physics and mathematics only

b-koefficienten — allmänt i sammandrag

2025¦2026

THE TNED RELATED NUCLEAR RADIOACTIVITY MATHEMATICS SETTLED

b-värdet bestäms (tabelleras) genom uppmätta värden på varje specifikt medelbaserad radionuklids tH och mE: dessa två kan INTE absolutberäknas, måste mätbestämmas,

DÄRFÖR att olika lokaler med olika preparat och olika mängder uppvisar inbördes influenser (+E’’) som i slutänden innebär att enbart (större, avgränsade) mängder preparat kan uppmätas för sina respektive medelbaserade sönderfall — vad vi vet. Normalvärdet med +E’=0 blir nominellt (som strängt taget aldrig gäller — men med avvikelser som är så små att de knappast kan mätas, normalt sett ..).

E = mv²/2 ; v² = 2E/m ; v = √2E/m ; mv = p = Ft = mat = m(v/t)t = mv = m√2E/m = √m²2E/m = √2mE ; (Se hela Härledningen till tH).

b-koefficienten blir (i den alternativa tolkningen) en ren nukleärt radioaktivt definierande parameter: b MaxMin är ±2(4pi) = ±25,13274123, med MaxMin Ñ = ±2 = ç/cz.

— DYNAMIKEN handlar om BALANSEN på ömse sidor om (Potentialbarriärens energizon: Applikation P78) cz = c0/2, stället där Q (Applikation 63) tas i den elektrofysikaliskt generella matematiska fysikens mening enligt TNED.

ç/cz = ç/(c0/2) = 2ç/c0.

— För stabila nuklider (ç=c0) gäller alltså en gränsform: Ñ = ±2.

— b-koefficienten påverkas (alltså) inte av ±E’ flöden. Medan de senare är rena Planckenergier (hf kvanta), baseras nuklidmassorna (b=±8pi) på rena g-baserade massdetaljer (PLANKRINGEN 2). Energiutbyten kan ske. Men Planckenergin

E = hf = mcr/t = mc² kan inte bilda gravitationens egenskap (P5), endast utföra dess sönderdelning i ljus och värme via (COEI) energins bevarande genom induktionsfysiken (Fysikens 7:e princip, P7). Se särskilt Integrala Analogin för massa (m) och induktans (L): Energiekvivalenterna, om ej redan bekant.

RadioAlphaEnergy: bKOFF

Varje (alfa) radionuklids sönderfallsenergi är/blir redan bestämd vid den nuklidens (exotermiska fusions-) bildning.

Bevis:

— skillnaden mellan atomvikterna före och efter. Dessa kan inte ändras:

— Here

(NucPro ¦ PointResult ¦ P5 ¦ P7 — principal structure of mass ¦ Application P72 — Planck energy¦ Application P73 ¦ Application P74 ¦ RanBam ¦ tIntegral ¦ NuclearInstability ¦ NKC)

we must omit the sublime ([fractal neutrino] omittable nuclear mass defect in E1818) influential radio nuclide’s emitting work energy

(m→γ: it demands, TNED says, a beyond [present] instrumental measuring capacity [»neutrino fractals», the neutron structure in Planck constant]).

— The unstable nuclide must perform WORK (»waste energy»: m→γ) as it rebuilds towards a — no losses — stable state before the Alpha particle is ejected. Schematically illustrated in Rfunction and SchemIllustr.

Sönderfallet sker INOM nuklidens egen marginella energiomsättning (försumbart, kan inte direkt mätas). Bevis: arbete (m→γ) måste utföras under kärnans instabila period, fram till utbrottet (samt vidare, om inte redan stabil).

— I LABORATORIETS REFERENS tillkommer sådana effekter som REKYLER vid utkastningarna — som kan variera marginellt beroende på.

• I den effektiva räkningen (händelsen sedd från moderkärnan) frånräknas rekylverkan.

RadioBirth: RadioAlphaEnergy

RadioBase ¦ StabUnstab ¦

• All nuclear radioactive atoms are born unstable:

• Independent of time to fission, the end effective fission energy equals the atomic mass difference between unstable-divided — minus the Alpha mass particle (atom).

— In established literature, it is (what we know) always the Alpha PARTICLE (the actual 2Helium4 nucleus). Never mentioned as the entire Helium Atom.

• t(Ñth) time taken until the Nth radio nuclide passes out (»birth moment») from the N₀ sample:

• 1st: 2tH; Last: 2tH(N₀) :

• What explains That Dynamics?

NALRadioTNED: RadioBirth

Rfunction

Nuclear-Alpha radioactivity, TNED physics

Consequential Mathematics:

— We just investigate the Mathematical possibilities. Without aspects of speculation or theory. Only what (we can relate) holds by known and well related math. Nothing else — or not at all.

No speculation. No Theory. No Consensus. RadioBase.

E = hf = mcr f = mc² = mc(r/[n→∞])[n→∞]f

[m=1¦ m]∑ [n→∞]f ; the Intensity increases with the Amount of (alike) individuals, Type U-238;

— The Intensity From Others hf Influence Function:

— speeding up the unstable nuclide’s necessary through-propagating fractal rebuild — before fission.

— Like irradiation on a Box from a distant lamp; it takes TIME to establish a certain heat degree inside the box (what comes in, must go ut); the more alike Lamps in the neighborhood, the faster the Settling Thermodynamic In-Box Condition.

— The higher Intensity — covered, and so certified, on all the radio nuclides in the Sample

— promotes a faster First Nuclide Individual splitting and leaving the Sample Radio nuclides; The Remaining Amount has then lost That Contribution, meaning

— Longer (mean-Life) for the next closest splitting nuclide. And so on. Down to the last:

• LONGEST MEAN-LIFE on least Intensity: only its own left.

Example:

— »We here in MAC Modern Academic Corridors know of nothing such as ’an endless fractal Planck constant nuclear structure’ .. ».

— Yes .. And .. ?

— .. But You CAN see the math of it .. or .. ?

RadioDisclaimer: NALRadioTNED

Without the nuclear fractal aspect (TNED) these statements and presentations have no meaning at all: statistics, probabilities. No explanation. Student’s nightmare: Perfect Intelligence — nobody home.

• All nuclear radioactive atoms are born unstable:

• Independent of time to fission, the end effective fission energy equals the atomic mass difference between unstable-divided, minus the Alpha mass particle.

• t(Ñth) time taken until the Nth radio nuclide passes out (»birth moment») from the N₀ sample: 1st: 2tH; Last: 2tH(N₀)

E = hf = mcr f = mc² = mc(r/[n→∞])[n→∞]f ; [m=1¦m]∑ [n→∞]f ;

m[n→∞]f = Increasing Intensity with m→∞ ; N₀/tH → 0 ; short first decay lifetime HIGH RATE

m[n→∞]f = Decreasing Intensity with m→1 ; N₀/tH → ∞ ; long first decay lifetime LOW RATE

RadioUnstableNature:

RADIOAKTIVITETENS KÄRNINSTABILA NATUR

The nature of radioactive nuclear instability

y = 0 + (0.1x)(sinx³) ¦ PREFIXxSIN ——————— x=sine; y¦=cosine:

Frequency modulated and increased Amplitude wave morphology.

The preferred illustrative interpretation.

— Nuclear instability begins from the highest possible frequencies (Compton effect), with lowest possible energies (RadioBase), evolving to lowest.

COMPARE THE BIRTH OF A STABLE NUCLIDE:

———————————————————————————— → ∞

Perfect nuclear surface charge stability

bKOFF ¦

RadioAlphaEnergy ¦ RadioBirth ¦ NALRadioTNED ¦ RadioDisclaimer ¦ RadioUnstableNature ¦

CalCard: Kalkylkort: — NOTE. OpenOffice SpreadSheet. Swedish EditionOnly

PART OF THE AIM behind these open available CalCards is of course

• first the availability of the proving mathematics on exact basics

• with the possibility for any interested reader to make own tests, or further, whatever

• offering a complete open access index to the complete work behind the main text :

• we leave no one behind in related physics and mathematics, as far as we can.

—————————————————————————————————————

THIS SWEDISH OPEN OFFICE CELL CODED VERSION —

we do not know how the cell code looks if opened in an English version — if at all ;

— We should have thought about that from the start [ 2008 ] — which we didn’t.

—————————————————————————————————————

Consequential Mathematics.

Further developed from 2023

NuclearSize2023c26.ods

kalkylkorten nedan DIREKT FRÅN DEN HÄR WEBBLÄSAREN NuclearSize2023c26.ods — se öppningsmanual om ej redan bekant — eller kopiera URL:en nedan till valfri webbläsare (vilket som fungerar — förutsatt att SVENSKA VERSIONEN av gratisprogramvaran OPEN OFFICE finns installerad på datorn)

http://www.universumshistoria.se/AaKort/NuclearSize2023c26.ods

CalculusCards OpenOffice SpreadSheet. Swedish EditionOnly

Tabell1 Constants — with: Basic TNED Toroid Math

Tabell2 Atomic mass tables (HOP¦ CODATA — Weizsäcker, see comparing The Resolution) with TNED toroid assessments

Tabell3 further Basic Toroid Math details (Tabl11 extensions .. drafts ..)

Tabell4 Atomic mass tables with further testing results .. Graphs and Diagrams ..

Tabell5 Comparing Hofstadter experiment Toroid results

Tabell6 Assessments with further Graphs (from Tabell5)

Tabell7 The composed Hofstadter Resulting Table

Kalkylkort ¦

Allmänna samband

END.

innehåll: SÖK äMNESORD på denna sida Ctrl+F · sök ämnesord överallt i SAKREGISTER

Universums Historia Aug2026 — Natur2026

ämnesrubriker

innehåll

SVERIGES SYSTEMATISKA NATURFÖRSTÖRELSE IIb

CWONsynth — COMPLETE WHOLE NUMBER SOLUTIONS — the isotopic distribution of the HONC elements in Earth mass AtmosBiosLitos — EarthBioNatureDetails

Recognition

Alt3

AP75

RelPM

TeClaNeaR — Aug2026 — TNED CLARIFYING NUCLEAR RESOLUTION

SummingJul2023

INTROrZ

rZ2023

rZ2023ER

BehindTNED

rZiteration

DiffRunits

Result

ErrorCheck

NeutronBegin

NeutronDetails

ConAtomic

AiLIE

CompiledNuclear

EXcon

KrischCollected

Wanted

NucPro

NucTNED

KingsTWO¦

NucDed — Nuclear Deduction

Corrections

CompiledToroidFormulae

AppliedToroMath

TopVdivTrans

Sources

ComparingExperimental

ToroSpinVolAR

FormulaeTEST

HOFtoro

TwelvePoints

N3View

PointResult

ToroNeutral

ResultsTable

RevisitHofP2

HOFTable

HofDiagrams

The2DM

HofEndResult

AKSAcollected

BottomLine

Physics7

APARC ¦ FUNTOP ¦ POM ¦ NEONS ¦ GRIP ¦ DEEP ¦ PASTOM

PBref ¦ ModernIQ ¦ EduModulus ¦

NUTGOMAD — NUCLEAR TOROID GEOMETRY MATHEMATICAL DETAILS

NEUTRON

General

NoVolMass

SpinResMech

NucSpin

TheNEUTRON

ResponBegin

TheResolution

LastQuest

TUNS — THE UNIVERSAL NATURE OF SPIN

SpinNature

PlanckConstant

NuclearSpin

ToroidFractal

CrimInvest

ComparingExperimental2

FurtherInquiry

GeneSpin

NoInnerLoss

MutualTRANSVERSEh

PCmain

FEC

NucleusDefinition

SpinPhysics

DisclaimingArg

TAN26 — THE ATOMIC NUCLEUS Aug2026 — TNED related physics and mathematics only

Morph

QImath

EnergyLAW

EquilibriumBalance

tIndependent

TAN

Provision

TanCon

SpinProperty

TanCons

SpinCon

ANExperimental

TANdetails

MassStructure

FractalTest

Eres

GrantProof

NeMo

rZ

rZSuggested

¦TheATOM

NeutronDecay

RanBam — RADIOACTIVE NUCLIDE BASIC MATHEMATICS

tIntegral

kFactor

RAA

tHproof

log2Fractal

INSERTINGk

NUCLEARb

SAMEXRAM — STRUCTURAL MATHEMATICS EXPLAINS RADIOMATH

StableUnstable ¦ SchemIllustr ¦ NuclearInstability ¦ bCoefficient ¦ JApplication ¦ pApplication ¦ ElectricForceLaw ¦ bCo ¦ SimpleEnergy ¦

NKCexplain — NEUTRINO KEY CODES (NKC)

NKC

RadioMathAug2026

StabUnstab

Graphs

Rfunction

bHspectrumOrigin — Original observations in H-spectrum, TNED editions from 2007

E1818

NucRanks

bcz

bCalc

bPrevious2017

bStatus2026

AlphaChan2017

bDeveloped

Radio2017

GeigerForm

RadioRelatedMAC

RadioRelatedTNED

InfectedTerminology

bKOFF — b-koefficienten — allmänt i sammandrag

RadioAlphaEnergy

RadioBirth

NALRadioTNED

RadioDisclaimer

RadioUnstableNature

CalCard

Senast uppdaterade version: 2026-09-01

*END.

Stavningskontrollerat 1Sep2026.

rester

*

referenser

[HOP]. HANDBOOK OF PHYSICS, E. U. Condon, McGraw-Hill 1967

Atomviktstabellen i HOP allmän referens i denna presentation, Table 2.1 MASS TABLE ¦ s9–65—9–86 ¦

concurrent with minor end decimal differences in Berkeley National 2003 and Nist/Codata 2005 — having no significance in this presentation

Comparing CODATA2005-HOP1967 ¦

m_n = 1.0086652u ...................... neutronmassan i atomära massenheter (u) [HOP Table 2.1 s9–65] — neutron mass

m_e = 0.000548598u .................. elektronmassan i atomära massenheter (u) [HOP Table 10.3 s7–155 för m_e , Table 1.4 s7–27 för u]

m(1H1) = 1.007825200u .................... neutronmassan i atomära massenheter (u) [HOP Table 2.1 s9–65]

u = 1.66043 t27 KG .............. atomära massenheten [HOP Table 1.4 s7–27, 1967]

u = 1.66033 t27 KG .............. atomära massenheten [ENCARTA 99 Molecular Weight]

u = 1.66041 t27 KG ............... atomära massenheten [FOCUS MATERIEN 1975 s124sp1mn]

u = 1.66053886 t27 KG ........ atomära massenheten [teknisk kalkylator, lista med konstanter SHARP EL-506W (2005)]

u = 1.6605402 t27 KG .......... atomära massenheten [@INTERNET (2007) sv. Wikipedia]

u = 1.66053906660 t27 KG .... atomära massenheten [@INTERNET (2023) en. Wikipedia, Atomic mass]

u = 1.660538782 t27 KG ...... atomära massenheten [från www.sizes.com],

CODATA rekommendation från 2006 med toleransen ±0,000 000 083 t27 KG (Committe on Data for Science and Technology)]

c₀ = 2.99792458 T8 M/S ......... ljushastigheten i vakuum [ENCARTA 99 Light, Velocity, (uppmättes i början på 1970-talet)]

h = 6.62559 t34 JS ................. Plancks konstant [HOP s7–155]

e = 1.602 · t19 C ...................... FOCUS MATERIEN 1975s666

G = 6.670 · t11 JM/(KG)² ........ FOCUS MATERIEN 1975s666 (6,67 · 10^–11 Nm²kg^–1)

[BA]. BONNIERS ASTRONOMI 1978

— Det internationella standardverket om universum sammanställt vid universitetet i Cambridge, The Cambridge Encyclopaedia of Astronomy, London 1977.

[FM]. FOCUS MATERIEN 1975 — Fysikens, kemins och astronomins historia. Allt från atomen till universum — fysik, kemi, jordvetenskap och astronomi

[BKL]. BONNIERS KONVERSATIONS LEXIKON, 12 band A(1922)-Ö(1928) med SUPPLEMENT A-Ö(1929)

t för 10^–, T för 10⁺, förenklade exponentbeteckningar

PREFIXEN FÖR bråkdelar och potenser av FYSIKALISKA STORHETER

Här används genomgående och konsekvent beteckningarna

förkortning för förenklad potensbeteckning

d deci t1

c centi t2

m milli t3

µ mikro t6

n nano t9

p pico t12

f femto t15

Alla Enheter anges här i MKSA-systemet (M meter, KG kilo[gram], S sekund, A ampere), alla med stor bokstav, liksom följande successiva tusenprefix:

K kilo T3

M mega T6

G giga T9

T tera T12

Exempel: Medan många skriver cm för centimeter skrivs här konsekvent cM (centiMeter).

MAC, här ofta använd förkortning för Modern ACademy (»Modern Academic Corridors») — etablerad vetenskap sedan början av 1800-talet

In UH often used abbreviation for modern academy — explicitly from the beginning of the 1800s

MAC — often used abbreviation in TNED for Modern ACademy

TNED — Related PHYSICS And MATHEMATICS from 1993 — Se särskild djupbeskrivning av innebörden i begreppet relaterad framställning.

Toroid Nukleära Elektro MEKANISKA Dynamiken —— Toroid Nuclear Electromechanical Dynamics

The Atomic Nucleus -- 1 - 4 ¦ TAN 1 ¦ TAN 2 ¦ TAN 3 ¦ TAN 4 ¦ TAN 5 ¦ AllKeplerMath ¦ AllKeplerMath+

ArithmeticResonanses:

FOR THE UNINITIATED READER (Sep2024):

On the 10Jan2024 the below (217) specified bPETRIE (1881-1883) finally proving resolution was discovered — after some research on eventually matching integer numbers. The 217 match certifies, as we see (from The rJCIRCLE complex ¦ rJCIRCLEref) the bPETRIE 4534.40 inch specified measure with a 99.9999832% precision. It is well enough to certify the accurateness on Petrie’s Cheops Pyramid measurements. That also consolidates the rJCIRCLE investigations on the subject;

— Taking present (mJ) EarthMass on the Planck constant h=mcr deduced Neutron density Dmax gives a spherical radius of (all natural constants, plus mJ) rJ = (h/c0)(3mJ/π·m⁴)^1/3.

The center of that sphere is precisely positioned in the sectional view of the Flinders Petrie group (1881-83) measures so called Queens Chamber in the Cheops Pyramid.

The GOLDEN SECTION complex from the simple form of Cheops Rectangle bd=h² proves

(CALTEP ¦ CaseHistory) the coherences in the Petrie measured Cheops Pyramid construct. The square corners enveloping that type defined Pyramid, passes precisely on the edge of the calculated rJ sphere’s surface. That was the initial discovery on the 1Nov2017. Really.

SOON ENOUGH — after a cup of Tea, relaxing on the new discovery, the 10Jan2024 — it was realized that the number 217 also connects to another Universal domain: UDHR10Dec1948. The Resolution 217(A) universal HumanRight declaration. It is also the absolute foundation (special case history) for this production in UniverseHistory (TNEDbegin1991).

We have two Resolution 217 in our known history — detailed to the last universal atom;

IN ORDER OF DISCOVERY-RECOGNITION — Resolution 217Short:

• Resolution 217(A) UDHR10Dec1948 — Universal Declaration of Human Rights: 8 introducing paragraphs P1-8,

30 following articles A1-30 — study them and try to learn them from within (test-question-analyze, 24/7).

— Here in UH referred to as Humanright, the only (reminded) known universal Humanright knowledge domain:

gravitation, electricity: light, heat, magnetism — LIFE: The Periodic System of The Elements (KeplerResonances).

— The Atoms’ Spontaneous assembly — no decision, no voting — to you and me (and all the other fuckups).

P1: ” Whereas recognition of the inherent dignity and ..”. Guaranteed Eternal Protection. 24/7. No breaks.

• Resolution 217 (10Jan2024) — the TNED deduced rJCIRCLE-CheopsPyramidEnvelopingSphereRadius (rJ) number

defines the actual Flinders Petrie 1883 measured Cheops Pyramid (half) base (b) — in to a precision of

99.9999832%. It verifies the (ContractedConstruct) TNED/Petrie investigated Cheops Building Plan: All Petrie’s measured values verified (BpointDetermination). The Complex (also, apparently: not much else left to chose on) connects to The Origin of Script. See TheCLAIM — questioning the already long ago 2000y questioned idea of a UNsanctioned Geographic Israel: (GUARD!) the splitting of humanity — and the Quest of its reunion.

(Toroid Nuclear Electromechanical Dynamics), eller Toroidnukleära Elektromekaniska Dynamiken är den dynamiskt ekvivalenta resultatbeskrivning som följer av härledningarna i Planckringen h=m_nc₀r_n, analogt Atomkärnans Härledning. Beskrivningen enligt TNED är relaterad, vilket innebär: alla, samtliga, detaljer gör anspråk på att vara fullständigt logiskt förklarbara och begripliga, eller så inte alls. Med TNED förstås (således) också

RELATERAD FYSIK OCH MATEMATIK. Se även uppkomsten av termen TNED i Atomkärnans Härledning.

SHORT ENGLISH — TNED in general is not found @INTERNET except under this domain

(Universe[s]History, introduced @INTERNET 2008VII3).

TNED or Toroid Nuclear Electromechanical Dynamics is the dynamically equivalent resulting description following the deductions in THE PLANCK RING, analogous AtomNucleus’ Deduction. The description according to TNED is related, meaning: all, each, details claim to be fully logically explainable and understandable, or not at all. With TNED is (hence) also understood RELATED PHYSICS AND MATHEMATICS. See also the emergence of the term TNED in AtomNucleus’ Deduction.

KALKYLKORTEN från Microsofts ordbehandlingsprogram (MsWORKS 4.0 | Från WINDOWS 95-eran) fungerar tyvärr inte utan vidare i webbformer (htm/html-filer). I denna presentation visas enbart kalkylkortets bild.

UTVECKLAT (Apr2010):

Samtliga kalkylkort med original från MsWors 4.0 finns nu i UNIVERSUMS HISTORIA. Se särskild beskrivning med förteckning i MANUAL.

Unicode (infört separat 23Jun2025):

≠ ≈ ∫ ∫ Δ √ Δ ≠ →γ ∞ Δ λ π √ ω ≈ π τ ε ħ UNICODE — ofta använda tecken i matematiska-tekniska-naturvetenskapliga beskrivningar

— Ctrl+Shift+Q i Microsoft WORD direkt till SYMBOL

σ ρ ν ν υ π τ γ λ η √ ħ ω →∞ →γ ≡ ¦ Alt+ 1..9 ☺☻♥☺♦♣♠•◘○ υ Ψ

Ω Φ Ψ Σ Π Ξ Λ Θ Δ ≈

α β γ δ ε λ θ κ π ρ τ φ ϕ σ ω ϖ ∏ √ ∑ ∂ ∆ ∫ ≤ ≈ ≥ ˂ ˃ ← ↑ → ∞ ↓ ↨Alt+23

ϑ ζ γ λ ξ

Pilsymboler, direkt via tangentbordet:

Alt+24 ↑; Alt+25 ↓; Alt+26 →; Alt+27 ←; Alt+22 ▬

Alt+23 ↨ — även Alt+18 ↕; Alt+29 ↔

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