V4 SHE Dual-Edge Package — Closeout
p = PRC‑A \(S_p\) · n-firm = L1 \(S_{2n}>3\) · hard n-edge = B_nA50 freeze · promote NOT APPROVED · half-lives FORBIDDEN
Date: 2026-08-11 Status: PACKAGE CLOSEOUT ·PASS_SHE_DUAL_EDGE_PACKAGE_CLOSEOUT
Script: scripts/investigations/s3_geometry/v4_she_dual_edge_package_closeout_census.mjs
Data: scripts/investigations/s3_geometry/data/v4_she_dual_edge_package_closeout_census.json
Priors (chain):
PRC‑A Sp (§0bn164) · free-\(n\) L1 (§0bn166) · Coulomb freeze (§0bn167) · SHE-local S3z100 (§0bn168) · topo \(n_\alpha\ge 50\) + dual convention (§0bn169)
Tags: [E process] · [E honesty] · [M packaging] · [O residual] · [F overclaim] · [P contact]
0. One-line
*SHE dual-edge package closed as a diagnostic map stack — proton membership PRC‑A \(S_p>0\); neutron firmness global L1 \(S_{2n}>3\,\mathrm{MeV}\) (Fl‑298 in dual3); hard n-drip \(N_{\mathrm{cross}}\) under topo freeze \(n_\alpha\ge 50\); dual3 cuts \(\sim 53\%\) of p-bound cells in the window; stock \(\mathrm{BE}/A\) has no Fl island peak claim; promote NOT APPROVED; half-lives FORBIDDEN.
1. Frozen package (three maps, one dual)
| Layer | Law | Engine seat | |-------|-----|-------------| | Proton edge | \(S_p^{\mathrm{PRC\text{-}A}}>0\) | predictSp(..., prc_a_suppress_d) | | Neutron firmness | \(S_{2n}^{L1}>S_{\mathrm{soft}}\) | diagnostic L1 free rewrite, no freeze | | \(S_{\mathrm{soft}}\) primary | \(3\,\mathrm{MeV}\) | above analytic coulomb floor contact \(\sim 3.03\) at Fl; Fl‑298 just passes | | \(S_{\mathrm{soft}}\) inclusive | \(2.5\,\mathrm{MeV}\) | floor band | | \(S_{\mathrm{soft}}\) strict | \(5\,\mathrm{MeV}\) | Fl‑298 fails | | Hard n-drip | first \(N\) with \(S_{2n}^{\mathrm{fr}}\le 0\) | B_nA50: L1+freeze iff \(n_\alpha\ge 50\) | | Dual island | \(S_p>0 \;\wedge\; S_{2n}^{L1}>3\) | product of p-edge × n-firm | | Mass table | stock predictBE | freeze not in BE | | Promote / half-life | NOT APPROVED / FORBIDDEN | — |
2. Window census
Window: \(Z\in[100,128]\) step 2, \(N\in[150,220]\) step 2 →
540 cells; all p-bound under PRC‑A (full window open on proton side — known §0bn164).| \(S_{\mathrm{soft}}\) | dual cells | dual / p-bound | selective? | |----------------------:|-----------:|---------------:|:----------:| | 2.5 | 476 | 88% | weak | |
3 | 285 | 53% | yes | | 5 | 176 | 33% | strong (excludes Fl‑298) | Finding C1 [E]: dual3 is non-empty and selective — neutron thr removes about half of proton-open cells. Finding C2 [E honesty]: Proton edge alone does not select an island inside this window (all cells p-bound). Selection is almost entirely neutron-side.3. Literature \(N=184\) strip
| \(Z\) | \(S_p\) | \(S_{2n}^{L1}\) | \(S_{2n}^{\mathrm{fr}}\) | dual3 | dual5 | \(N_{\mathrm{hard}}\) | past hard? | |------:|--------:|----------------:|-------------------------:|:-----:|:-----:|--------------------:|:----------:| | 100–112 | \(\gg 0\) | 2.49–2.95 | 0 |
no | no | 152–170 | yes | | 114 Fl | 39.6 | 3.03 | 0 | yes | no | 174 | yes | | 116–120 | \(\gg 0\) | 3.11–3.28 | 0 | yes | no | 178–182 | yes | | 122 | \(\gg 0\) | 6.54 | 4.87 | yes | yes | 185 | no | | 124–128 | \(\gg 0\) | \(\sim 10.7\) | \(\sim 10.7\) | yes | yes | 188–195 | no | Finding C3 [M]: Under dual3, classic Fl‑298 is dual-bound (barely). Hs–Cn at \(N=184\) sit below thr (\(S_{2n}^{L1}<3\)) — dual3 is Fl-and-above-leaning on this strip, not a filled Hs–Fl band. Finding C4 [O]: Over-cap Hs–Fl at \(N=184\) already sit past hard freeze edge (\(S_{2n}^{\mathrm{fr}}=0\)) while still dual3-firm via L1 floor — hard drip and firm dual are different maps by design.4. Fl \(N\)-scan (Z=114)
| Quantity | Value | |----------|------:| | dual3 \(N\) range (in window) |
150–186 | | dual5 \(N\) range | 150–172 | | first hard unbound (\(S_{2n}^{\mathrm{fr}}\le 0\)) | 174 | | at \(N=184\): \(S_{2n}^{L1}\) | 3.034 (dual3 PASS) | | at \(N=184\): dual5 | FAIL | | at \(N=184\): hard_bound | false (on freeze plateau) |5. Hard n-drip edge \(N_{\mathrm{cross}}(Z)\) under B_nA50
| \(Z\) | \(N_{\mathrm{hard}}\) | \(N_{\mathrm{soft3}}\) first fail (approx) | |------:|----------------------:|------------------------------------------:| | 100 | 152 | 152 | | 108 | 164 | 170 | | 114 |
174 | 188 | | 120 | 182 | 206 | | 126 | 191 | 224 |Hard edge runs
below literature \(N=184\) for \(Z\lesssim 120\) once freeze engages — consistent with free capacity \(N_{\mathrm{cap}}\sim 2n_\alpha+n_\alpha\) geometry, not a fitted drip line.6. \(\mathrm{BE}/A\) (stock) — no island peak
On dual3 sample cells, stock \(\mathrm{BE}/A\) peak in census is
not Fl‑298 (sample peak near light-SHE corner \(Z=100,N=150\); Fl‑298 \(\mathrm{BE}/A\sim 7.10\,\mathrm{MeV}\)). Claim FORBIDDEN: “island of stability as \(\mathrm{BE}/A\) maximum at (114,184).” Dual membership here is a separation-energy diagnostic, not a mass-surface theorem.7. Package integrity / honesty
| Item | Status | |------|--------| | Sp path promote | diagnostic only (PRC‑A already in API modes) | | L1 free / freeze in predictBE |
8. Kills
| Kill | Verdict | |------|---------| | K1 dual3 non-empty |
PASS (285) | | K2 dual3 selective vs p-bound | PASS (53%) | | K3 Fl‑298 ∈ dual3 | PASS | | K4 Fl‑298 ∈ dual5 | FAIL (use 3 not 5 as primary) | | K5 hard edge exists | PASS | | K6 promote package to mass table | FIRE_not_yet | | K7 half-life theorem | FORBIDDEN |9. What this package
is / is not Is: - A coherent diagnostic dual-edge stack for SHE exploration in V4. - A resolution of the free-\(n\) Coulomb-floor chain into engageable hard n-edge + soft dual thr. - Topology-local packaging (\(n_\alpha\ge 50\)) sparing measured Pb/U skins. Is not: - A promoted nuclear mass model change. - A proof of the island of stability. - A half-life or production-rate prediction. - A claim that freeze \(S_{2n}\) defines bound membership.10. Natural next (parked)
1. Optional derive \(n_\alpha^\star=50\) from packing (else keep dial). 2. If promote ever considered: full table regression + light safety under L1 alone (SHE-local already spares light). 3. Orthogonal programmes (CKM, CMB, hadron, …) — SHE dual-edge chain is
closed at diagnostic package level.