Research note (no κ): T74 #2322 words — owner fills capped at b < 0.001697195759 (#2374 within 8.1e-10); exact prices of handoffs, aliases and rank-1 climb merges

[thakrarsagar]

Research note (no κ claim). For the #2322 T74 words (base of the open #2349 / #2363 / #2374 line), this certifies the remaining owner-fill headroom and gives exact prices for local inventory moves.

finding (LP-ceiling differences on the #2322 words, both providers, at a = #2374's κ)	value
certified cap, any legal whole-helper owner fill of the #2322 words	b < 0.001697195759
headroom above #2374's claim (0.0016971949509)	≤ 8.1e-10
one more #2322-type handoff (same reshapes)	+4.27e-8 each, linear up to 12 (+5.13e-7)
one #2339-type low alias	−1.91e-7
one #2339-type high alias	exactly 0
one (1,1)→(2) merge of two rank-1 climbs (no width change)	+1.13e-7
the 26 such target merges that come with #2339's low aliases, on their own	+2.94e-6

Why. A climb of d dimensions pays one child of rank d, and total rank mass is fixed. So a move changes b only through the shape of the paid children, plus the helper widths acting through the width-aware bin patterns of #2387 / #2360.

• Cap. It comes from the 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 #2387 LP with an exact rational dual and 800-bit enclosures (W·mu margin 1.85e-7, zero dual repair). The certificate does not reject Conditional κ = 0.001697194950901770: exact owner fill on #2322's handoff construction #2374's claimed point. Owner relocations on these words therefore have at most 8.1e-10 left.

• Conditional κ = 0.001696891067241618: helper width exchange on the borrowed T74 words #2312 → Improve conditional κ to 0.001697060296258836 with coherent handoffs and retimed hosting #2322 decomposes exactly into four handoffs:

  • remove (1,1,1,1) helpers 619/621/622/623;
  • X lenders 1/4/6/12 go (5,1,1,1)→(2,1,1,1,1,1,1);
  • partners 616/617/618/620 go (4,1,1,1,1)→(3,2,1,1,1).

  The LP predicts a +1.96e-7 ceiling gain; the realized claims gained +1.69e-7.

• 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 → Construction (no κ claim): PR2226 low anticipatory aliases on the T74 borrow words — 400 helpers, mass 5264, packing ceiling 0.0017179→0.0017480 #2339 decomposes exactly.

  • A low alias's lender takes over the helper's climb, a net −h(3) locally, but the width change costs more through the bins.
  • A high alias is exactly neutral.
  • The 26 changed targets each gain exactly one (1,1)→(2) merge. These merges alone would be worth +2.94e-6, which dwarfs the owner-fill race.

Leads (priced, not constructed).

• 33 helpers still climb (1,1,1,1): the 32 Research: 80-helper anticipatory borrowing component and exact price rejection (no new kappa) #2226 low lenders plus 653.
• 12 X registers still climb (5,1,1,1) and lend no warp: 31 33 49 55 68 74 80 83 85 88 98 101.
• Block 53 has exactly Improve conditional κ to 0.001697060296258836 with coherent handoffs and retimed hosting #2322's pre-handoff pattern: 653 next to four (4,1,1,1,1) partners 648/649/650/652. Conditional κ = 0.001697194950901770: exact owner fill on #2322's handoff construction #2374 notes that alias 653 was dropped.

Whether any of these admits a legal coherent handoff is not checked here; it is listed under open next questions.

Checks.

• move_prices.py recounts which register pays each child in 8 pinned words. Each recount equals the word's reported profile and width inventory, and the decompositions add up exactly. Controls cover move signs, high-alias neutrality, the mass identity, and the certificate not rejecting Conditional κ = 0.001697194950901770: exact owner fill on #2322's handoff construction #2374.
• independent_recount.py was written by a separate AI reviewer subagent from a plain statement of the frame rules, with its own GF(2) code and no shared code. It reproduces the profiles, the change set and the site lists for both providers.
• Package metadata (--check-only) passes; 65/65 research tests pass (2 skipped); 3.10 grammar check passes.
• Everything was run on CPython 3.14.4. The registered 3.12 replay was not run locally.

Reproduce (standard library only; --fetch pulls refs/pull/{2312,2322,2269,2339}/head if commits fb76f79 / 002304e / b479fc5 / bf1742a are absent; every word file is blob- and sha256-pinned):

python3 -I -B research/t74-2322-move-prices/move_prices.py --fetch   # ~16 s -> PASS_T74_MOVE_PRICES cap=0.001697195759 handoff_db=+4.272e-08 low_alias_db=-1.906e-07 high_alias_net=0 sites=33/12
python3 -I -B research/t74-2322-move-prices/independent_recount.py   # -> PASS_T74_INDEPENDENT_RECOUNT

vendor/pr2387/ holds pinned byte copies of #2387's ceiling_lp.py and fill_check80.py (this author). move_prices.py patches one line of local_recount at load time, to record the register that pays each child.

Scope. This is a pricing screen on fixed pinned words. Windows, families and ports are dropped, so prices are ceiling differences, not realized gains. The cap is a relaxation ceiling for unsplit helpers on the unchanged #2269 bin stock. No handoff or merge is constructed, and the selected frontier is untouched. Base: canonical main 0fdd7d82. Task card: complex-new-helper-inventory, scope refined.

Credits.

• 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 = 0.001696247139058474: 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.
• 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 jeremykothe2 and Improve conditional κ to 0.001697147064845350 with whole-role augmenting paths #2363 mason-hale.
• Research: 80-helper anticipatory borrowing component and exact price rejection (no new kappa) #2226 Cinna Davis.
• Certify PR2339's whole-helper T74 packing cap below 0.0016870 #2360 Jeremy Diviney and Conditional κ = 0.001674097969905390: an attaining T37 construction and fixed R480 owner optimum #1129 Ali Romman (pattern dual).
• Research: lower PR #2339's initial T74 prefix with 64 monomial applications #2394 commdata2338 (native anticipatory prefix).
• Research: bound joint helper-end and frame contractions of the selected k8 word #1995 / Research: bound arbitrary helper terminal frames of the selected k8 word #2013 (fixed-word frame bounds).
• Conditional kappa 0.001676855229071321: verified exact fill on 74 replicas #1319 / Conditional kappa 0.001676854978651125: four composed helper-donor cold kernels #1297 T74 lineage.

Prepared with substantial AI assistance (Claude Code, Anthropic, Claude Opus 5.5). No independent human review is claimed. Apache-2.0.

🤖 Generated with Claude Code

[thakrarsagar]

Follow-up commit a419c99 answers open question 2 (target merges without low aliases) with merge_mechanism.py.

• Mechanism. Checked on all 26 merged targets in both providers:
  • Each target skips exactly one dimension-1 frame.
  • Every gate at that frame in 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 comes from a helper that Construction (no κ claim): PR2226 low anticipatory aliases on the T74 borrow words — 400 helpers, mass 5264, packing ceiling 0.0017179→0.0017480 #2339 removes (104 gates, 32 helpers).
  • Each target is instead fed by Construction (no κ claim): PR2226 low anticipatory aliases on the T74 borrow words — 400 helpers, mass 5264, packing ceiling 0.0017179→0.0017480 #2339's frame-0 anticipatory corrections. 26 of the 32 corrected targets merge.
• Lenders. A frame-0 lender that takes over a FULL-ending role must end FULL, so its width becomes 9 (= H). On the Improve conditional κ to 0.001697060296258836 with coherent handoffs and retimed hosting #2322 words the frame-0 helpers end at dimensions {4: 32, 7: 8, 8: 8, 9: 240}. The 32 that end at dimension 4 are exactly the Research: 80-helper anticipatory borrowing component and exact price rejection (no new kappa) #2226 lenders.
• Rank-zero route is closed. Under rank-zero borrowing, the merges come only with the width-4 → 9 lender change. Each such alias loses −1.9e-7, and still −7.8e-8 with a merge credited, so the merges cannot be separated from that change.
• Changed premise, priced. Take-overs by the 16 frame-0 lenders ending at dimension 7–8 are outside rank-zero, per Construction (no κ claim): PR2226 low anticipatory aliases on the T74 borrow words — 400 helpers, mass 5264, packing ceiling 0.0017179→0.0017480 #2339's handoff screen. They are priced at up to +1.43e-6 each on the Improve conditional κ to 0.001697060296258836 with coherent handoffs and retimed hosting #2322 words, before the cost of raising the role's gate frames. That replaces question 2 as the new open question.

A separate subagent reviewer re-derived the mechanism and the census with its own code and agreed in both providers. Expected line: PASS_T74_MERGE_MECHANISM merged=26 lenders_end4=32 pr2339_alias_db=-7.792e-08 takeover8_db=+1.427e-06.