Negative result (no κ): legal 400-helper owner fill of #2339's 80-alias T74 words reaches b = 0.00168654, 99.994% of a certified width-aware cap b < 0.0016867 — below #2269

[thakrarsagar]

Negative result (no κ claim). This builds and prices an actual legal owner fill for the #2339 80-alias T74 words. It also certifies a width-aware ceiling for every such fill. Both lie below #2269, so the low-alias inventory is cost-negative on the unchanged T74 template.

object	b
#2339's estimate (width-blind cap × #2269's realized fraction)	≈ 0.0017259 (wrong)
width-blind R = 48 cap (merged complex-local-word-ceiling)	0.0017479583719744
certified width-aware ceiling, any legal whole-helper fill	< 0.0016867
realized legal fill OWNERS-80 (native, bracket width 1e-40)	0.00168654323626906426826…
#2269 claimed b	0.00169624713905847422…

What was learned. The low aliases free 121 local rank units per call. But they swap width-8 helpers, which pack exactly into the rank-8/16/32 bins, for width-9 lenders. In the LP optimum, 27,824 rank-32 bins then host [9,9,9] and keep a rank-5 idle child, and 6,068 rank-16 bins host a lone [9] and keep a rank-7 child. That fragmentation costs more than the freed mass.

The fill realizes 99.994% of its ceiling, so better packing cannot rescue it. The "+5 high aliases" give exactly zero gain: each one turns a local rank-5 child into an idle rank-5 remainder, and the ceiling equals #2269's to all digits. Positive controls: #2269 realizes 99.991% of its own ceiling (b < 0.0016965), and #2322 realizes 99.992% (b < 0.0016973). Neither is rejected at its claim.

Overlap. #2360 (Jeremy Diviney) independently certifies b < 0.0016870 for the same words with the same 1,163-pattern relaxation; it appeared while this was in progress. This PR adds:

• the attainable side: a legal 266,400-role fill, independently recounted;
• a tighter certificate from the real 249/417 dispatch (b < 0.0016867 vs < 0.0016870);
• the variant and control cases;
• an independent re-check of Certify PR2339's whole-helper T74 packing cap below 0.0016870 #2360's DUAL.json: 1,163/1,163 inequalities hold, the lower bound of 66304·mu is 66304.0043 under its envelope, and a tampered dual is rejected.

The relaxation method comes from #1129 (Ali Romman) and the R480 pattern-dual audit.

Checks.

• fill_check80.py is standalone, adapted from our Independent verification (no new κ): record candidate #2269 T74 borrow43 — words, 437-helper fill and moment root reproduce; stale evidence, unpriced buffers, X2 open #2315 checker. It recounts OWNERS-80 against the pinned Construction (no κ claim): PR2226 low anticipatory aliases on the T74 borrow words — 400 helpers, mass 5264, packing ceiling 0.0017179→0.0017480 #2339 words and the Conditional κ = 0.001696247139058474: capped phase-cell fusion outer (PR1673) on the T74 supplier with anticipatory dirty borrowing (PR2226, 43 high-helper aliases) on the T74 pivot-566+554 supplier: conditional kappa 0.0016962471390584742… #2269 GLOBAL-TEMPLATE under rules R-a..R-g:
  • widths and one role per helper;
  • capacity and prefix-filled slices;
  • idle and profile recount;
  • roles strictly inside rebuilt windows;
  • families: owner·896 + (2·pair+side)·112 + port, never the caller's active pair;
  • Improve conditional κ to 0.001697060296258836 with coherent handoffs and retimed hosting #2322's private namespace (physical 66714, 44 buffers in reserve);
  • X2 pending-axis disjointness and 3,175 73-column charts.
• It rejects 16 mutations and accepts Conditional κ = 0.001696247139058474: capped phase-cell fusion outer (PR1673) on the T74 supplier with anticipatory dirty borrowing (PR2226, 43 high-helper aliases) on the T74 pivot-566+554 supplier: conditional kappa 0.0016962471390584742… #2269's own fill as a positive control.
• price80.py gives the 1e-40 native and conservative brackets, with 12 controls; the fill is rejected at Conditional κ = 0.001696247139058474: capped phase-cell fusion outer (PR1673) on the T74 supplier with anticipatory dirty borrowing (PR2226, 43 high-helper aliases) on the T74 pivot-566+554 supplier: conditional kappa 0.0016962471390584742… #2269's b and at Improve conditional κ to 0.001697060296258836 with coherent handoffs and retimed hosting #2322's κ.

Reproduce (standard library only; --fetch pulls refs/pull/2269/head b479fc5 and refs/pull/2322/head 002304e if absent):

python3 -I -B research/t74-80alias-owner-fill/run_all.py --fetch   # ~25 s -> PASS_T74_80ALIAS_RUN_ALL roles=266400 ... below_2269=1 below_2322=1
python3 -I -B research/t74-80alias-owner-fill/ceiling_lp.py        # ~7 s  -> PASS_T74_WIDTH_AWARE_CEILING

The #2339 words come from commit bf1742a when present, otherwise from blob- and sha256-pinned copies in inputs/. The rebuild (build_fill.py, about 230 s, deterministic) is optional.

Pins.

• Base: canonical main 0fdd7d82.
• Task card: complex-new-helper-inventory, scope refined to this inventory.
• Package metadata (--check-only) passes; 65/65 research tests pass (2 skipped).

Environment. Everything was run on CPython 3.14.4 (Linux), plus a 3.10 grammar check. The registered 3.12 replay was not run locally because 3.12 is unavailable here.

Scope. This is a finite fill plus a scoped relaxation ceiling for the fixed #2339 words, unsplit helpers and the unchanged #2269 bin stock. It is not an impossibility result for partial alias subsets, a changed bin stock, split reservations or a changed local contract; these are listed as open next questions. Native lowering of the 64 initial corrections and 37 warps, lender lifetimes, X-field ownership, buffers, prefix bits, the PLAN/SPEC refreeze and the outer ledger remain unchecked. They cannot help, because the fill already loses. The selected frontier is untouched.

Credits.

• Construction (no κ claim): PR2226 low anticipatory aliases on the T74 borrow words — 400 helpers, mass 5264, packing ceiling 0.0017179→0.0017480 #2339 (this author).
• Conditional κ = 0.001696247139058474: capped phase-cell fusion outer (PR1673) on the T74 supplier with anticipatory dirty borrowing (PR2226, 43 high-helper aliases) on the T74 pivot-566+554 supplier: conditional kappa 0.0016962471390584742… #2269 Jeremy Kothe.
• Improve conditional κ to 0.001697060296258836 with coherent handoffs and retimed hosting #2322 Vlado Vojdanovski.
• Conditional κ = 0.001696891067241618: helper width exchange on the borrowed T74 words #2312 / Conditional κ = 0.001696395766736081: exact pivot-518 and 506 helper-donor kernel(s) (PR1625 shape, KernelsOnBorrow) on the borrowed words, exact frame refit (WildIdeas), 1e-3000 certified supplier endpoint, fixed-grid-maximum kappa C - 1/… #2302 jeremykothe2.
• Research: 80-helper anticipatory borrowing component and exact price rejection (no new kappa) #2226 Cinna Davis.
• Conditional kappa 0.001676855229071321: verified exact fill on 74 replicas #1319 / Conditional kappa 0.001676854978651125: four composed helper-donor cold kernels #1297 T74 lineage (Rohan Arun et al.).
• Douglas Colkitt's cap model.
• Certify PR2339's whole-helper T74 packing cap below 0.0016870 #2360 Jeremy Diviney (concurrent; DUAL.json copied byte-for-byte).
• Conditional κ = 0.001674097969905390: an attaining T37 construction and fixed R480 owner optimum #1129 Ali Romman.
• Conditional κ = 0.001697194950901770: exact owner fill on #2322's handoff construction #2374 / Conditional κ = 0.001697065994108880: owner relocations on #2322's handoff construction #2349 / Improve conditional κ to 0.001697147064845350 with whole-role augmenting paths #2363 are cited as reference points.

Prepared with substantial AI assistance (Claude Code, Anthropic, Claude Opus 5.5). An AI subagent reviewed the fill checker; no independent human review is claimed. Apache-2.0.

🤖 Generated with Claude Code