Nuclear physics
The claim that magicity migrates with neutron–proton asymmetry, tested on measured masses only — 28% of the mass table is estimated and was discarded.
Do nuclear shell closures shift with asymmetry?
Hypothesis H141, Volume XII — "Shell closures shift with asymmetry" <https://incoprea.com/research-library/original-theories-vol12-20261030/> · 30 October 2026 · not peer reviewed · AI-assisted
Result
The gap at a magic neutron number does vary between isotopes — ranges of 1.6 to 3.98 MeV in the five shells tested — so half the claim survives. It is not systematic in asymmetry (N−Z)/A: with N fixed effects and a proton-magic control, b = −2.14 ± 1.02 MeV per unit asymmetry, bootstrap CI −4.66 … +0.62, within-N permutation p = 0.094, partial R² 0.061. The decisive fact is the sign flip: the within-shell slope runs from −7.1 MeV at N = 20 to +24.4 MeV at N = 126. The third prediction holds — the five proton-magic isotones sit +1.38 ± 0.28 MeV high (p = 0.00015). Verdict: the asymmetry mechanism is refuted; the phenomenon is not.
Design
AME2020 masses, parsed by fixed-width column after hand-inspecting the header (SOURCE.md). Of 3,558 data rows, 1,008 (28.3 %) carry the # estimated-mass flag and were discarded; 2,550 remain. The brief's statistic, exactly as written,
S2n(Z,N) = M(Z,N−1) + Mn − M(Z,N), D2n = S2n(Z,N) − S2n(Z,N+2), Mn = 8.0713171 MeV,
for N ∈ {20, 28, 50, 82, 126} and every isotone with all four masses measured: n = 75 (12, 12, 19, 20, 12 per shell). Five rows would have needed an imputed N−1 mass (6.25 %, over the 5 % gate): none was imputed. Families, each Benjamini–Hochberg adjusted once: A five within-N Spearman tests, B four within-shell proton-magic vs rest permutation tests, C two slopes.
Table 1 — spread at fixed N
| 20 | 0.17 | 1.71 | 4.15 | 1.10 | 3.98 | 0.83 |
|---|---|---|---|---|---|---|
| 28 | 1.82 | 2.99 | 4.43 | 0.90 | 2.60 | 0.71 |
| 50 | 1.95 | 2.74 | 3.56 | 0.38 | 1.61 | 0.38 |
| 82 | 1.86 | 2.10 | 3.72 | 0.49 | 1.87 | 0.40 |
| 126 | 0.70 | 1.48 | 2.32 | 0.88 | 1.62 | 0.82 |
MeV (spread_by_shell.csv). P1 — supported on the range (1.61–3.98 MeV, all five shells), not on the IQR bar: 0 of 5 exceed 1.5 MeV.
P2 — refuted: the trend changes sign
| N fixed effects | 75 | −2.267 | 1.172 | 0.128 | −5.10 … +0.93 | 0.381 | — |
|---|---|---|---|---|---|---|---|
| + proton-magic | 75 | −2.141 | 1.016 | 0.094 (q = 0.128) | −4.66 … +0.62 | 0.543 | 0.061 |
b in MeV per unit (N−Z)/A; OLS, within-N permutation p (20,000 permutations, seed 7), row bootstrap (20,000 draws, seed 11); family C, m = 2. Within-shell Spearman rho: −0.63 at N = 20 (q = 0.054), −0.02 at N = 28 (q = 0.96), −0.44 at N = 50 (q = 0.072), +0.82 at N = 82 (q = 0.0003), +0.92 at N = 126 (q = 0.0006); family A, m = 5. Pooled without N fixed effects, r = −0.34 (p = 0.0035) — between-shell structure.
P3 — supported, on thin data
The five proton-magic isotones sit +1.384 ± 0.282 MeV above the rest at the same N (t = 4.90, permutation p = 0.00015, analytic CI 0.82 … 1.95), spanning asymmetry 0.00 to 0.24 — not an asymmetry trend in disguise. Within-shell, with one or two magic rows each, the tests are powerless: p = 0.084, 0.048, 0.050, 0.250; q = 0.112, 0.099, 0.099, 0.250.
Definitional fork (post-hoc)
The brief's S2n is algebraically the one-neutron separation energy, so its D2n is a first difference of S_n and keeps the smooth trend in it; the conventional gap is a second difference and removes it (r = 0.89 between them, means differing by 2.1 MeV). With Δ2n = M(Z,N−2) − 2M(Z,N) + M(Z,N+2), n = 73: b = −7.46 ± 1.79, p = 0.0022, CI −11.47 … −2.14, IQR above 1.5 MeV in 3 of 5 shells — which would meet the support criterion. The briefed formula stands as primary and refuted; the gap definition, not the data, decides P2.
What the test cannot see
A mass table measures mass differences, not shell structure: a large D2n fits a closed shell and a deformed intruder equally, so nothing here says whether N = 50 is "magic" in a given nucleus. Mass uncertainties (1–100 keV) were not propagated; they are one to two orders below the spreads reported, but that is an argument, not a measurement. Asymmetry varies little inside a shell (0.06 at N = 126 against 0.34 at N = 20), so the slope rests mainly on the light shells.
What would change the answer
A clean second-difference gap definition — it exists, and reverses P2 — plus more proton-magic isotones with measured masses, which AME2020 does not supply.
Files
run.py · results.json · data/ · figures/ (Figures 1–3) · hypothesis.md · SOURCE.md.
Disclosure: designed and executed with AI assistance (DeepSeek, via its coding agent), not peer reviewed. Observational associations in published nuclear mass data only; no medical, clinical, financial or safety advice.
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