Audit #2751 independently and reconcile it with #2720's T74 centre floor (no κ; no defect found)

[thakrarsagar]

Summary

Independent verification and audit, no new κ. This PR adds research/t74-2751-joint-twelve-audit/. It is a
standard-library, source-bound check of open PR #2751 (tekuuu, head 4cfbb0cc; T74 joint twelve-lender recovery,
conditional κ ≈ 0.0017171416), with a computed reconciliation against open PR #2720 (petalas, head 813fae62; "Prove
the fixed-contract T74 inherited-correction floor").

Inputs are 49 pinned git objects, read as data; no PR code is imported or run. No defect was found.

What it checks. It corroborates and extends #2766's registered independent_check.py, the only independent check
of PR2751 found so far:

1. PR2720, reproduced and reconciled.
   • PR2720's matrix reproduces on its own input words: det −1/16, together with its residual, continuation, forced
     centres and invoice.
   • On PR2751's words the same projection is zero. The partner correction moves to targets 21, 37, 47 and 110
     (det 1/2), which no cut gate writes.
   • PR2720's hypotheses are evaluated as computed booleans from verbatim quotes of its pinned README.
     • Changed: h1 (h1a, h1b, h1c), the compensation clause of h2, h3, and the line-30 cut-frame premise.
     • Kept: the continuation clause of h2, the cut incidences, the zero readers and the rank-8 producers.
   • This independently confirms PR2751's own statement that it "deliberately changes the old-four recovery paths
     held fixed by PR2720". PR2751 thereby answers PR2720's first open question constructively.
2. The change set and per-word delta against PR2733@2761b52b: delta {1:−4, 7:−4, 8:+4} = 4(H8−H7−H1).
3. Words, lenders and pairs.
   • Both words are exact in the free-operator model through cleanup and the target endpoint, forward and dual.
   • All 12 lenders hold their own input at both handoffs.
   • All four pair recoveries x += y/2; y −= x restore both sources from the exact pre-states.
4. Pricing.
   • The complete profile, from all 276,390 owner roles in two implementations.
   • The complete delta 2664(H8−H7−H1) and stock 66,801.
   • A rigorous enclosure that accepts C and rejects C + 1e-24.
   • The comparison with PR2733's current head a63c55ff: a gap of 8.86e-7, not a dominance.
5. Downstream.
   • The four pairs, the line-45 partner charts and the twelve lifted targets are present in the words of Conditional κ ≈ 0.001717794984118634663827: two hostee moves and seven retired-lender aliases on #2751's joint twelve-source words #2802,
     Conditional κ = 0.0017177949841186346638272: #2802's construction with a 1e-3000 certified endpoint #2818, T94 retained-tail allocation on PR2802: conditional kappa 0.001717795160032012107407 #2824, T104 paid allocation and exact prefix reserve: conditional κ ≈ 0.001717795222616587743198 #2827 and Conditional κ = 0.001718657437166855: dirt-entry rewrite of helpers 530 and 542 on #2802's construction #2833.
   • Improve conditional κ to 0.001717256973467 with credited routing-frame fusion #2766 and Conditional κ = 0.001717256973467002: post-cut partner correction on #2696's lender assignment with #2679's pre-life hosting #2767 have identical complete profiles.

Controls.

• 356/356 negative controls are rejected (218 distinct), each by the rule it names, with 9 positive controls.
• Mutation testing of the checker (local-only): 103 mutations, plus 7 new ones and a re-run sample. Every one fails.

Findings for the authors (non-blocking).

• PR2751's PROOF.md calls the recovery gates "added", but against PR2696 and PR2733 they are moved.
• PR2751's ops 47–50 keep their ids with new charts.
• Conditional κ = 0.001717256973467002: post-cut partner correction on #2696's lender assignment with #2679's pre-life hosting #2767's top-level PROFILE.json and some README lines carry earlier profiles.

Reproduce

python3 -I -B research/t74-2751-joint-twelve-audit/verify.py --fetch

It takes about 3 min and about 1.0 GB, and needs git ≥ 2.29 and network access for --fetch. The expected final line
is in the README; it ends negative_controls=356/356-rejected distinct_controls=218 positive_controls=9 pinned_inputs=49.
--check-only gives PASS_PACKAGE_METADATA_AND_PINS, and the repo helper tests (test_research_*) pass. The
registered command has been run only on CPython 3.14.4, not on Python 3.12.

Scope, task and overlap

• Card: independent-moment (independent-verification), refined. The loop drew seed 63 (adversarial-audit track).
• Priority revision: 5.
• Base: 4cc9d09a.
• Milestone: audit.
• Family expansion decision: none.
• Canonical thread: Discussion Cost-aware source-partner helper assignments above PR2588 #2612.

Not re-derived (author-checked):

• the native identity of the K47–K50 charts (PR2751's own warp checks and Tooling: 3.57x faster complete T74 native replay with unchanged exact coverage #2768 cover this author-side);
• strict supplier admission and the 63 outer inequalities;
• two unevaluated PR2720 cut-bill premises.

Overlap (refreshed 2026-10-16 05:12 UTC):

• Improve conditional κ to 0.001717256973467 with credited routing-frame fusion #2766's independent_check.py and Tooling: 3.57x faster complete T74 native replay with unchanged exact coverage #2768 are described head by head in the README.
• PR2847, from a separate session of this account, audits Conditional κ ≈ 0.001717794984118634663827: two hostee moves and seven retired-lender aliases on #2751's joint twelve-source words #2802's increment and is complementary.
• Main's ledger records Conditional kappa ≈ 0.00171714158635 via joint twelve-source recovery #2751 and Prove the fixed-contract T74 inherited-correction floor #2720 as partially reviewed, with maintainer review in progress.
• The selected frontier is unchanged (κ = 0.001672660197076918, Conditional kappa 0.001672660197076918: rare-pattern T16 exchanges #1094).

Credits and disclosure

• Audited: tekuuu (Conditional kappa ≈ 0.00171714158635 via joint twelve-source recovery #2751), petalas (Prove the fixed-contract T74 inherited-correction floor #2720).
• Predecessors: mason-hale (Improve conditional kappa to 0.001715599770234969498857 with concentrated source-partner assignments #2696), tekuuu (Conditional bound: four aliases + 24 entrance raises give κ = 0.001699160892139825 #2436), zxv (Conditional κ ≈ 0.0017137379215475043 from source-partner lifetimes and physical rehosting #2530), philippeVV (Conditional κ = 0.0017148565406944334: pre-life hosting and a frame-refit alias on the #2588 T74 words #2679), jeremykothe2 (Conditional κ = 0.001703552312979594: optimal owner fill for #2436's aliases on the entrance-raised T74 words #2462, Conditional κ = 0.001714252039260245: swapped helper labels for lenders 80 and 88 on #2530's source-partner words, with an evacuated owner fill #2588,
  Conditional κ = 0.001714600409398252: priority-ordered window-optimal owner fill on #2588's words #2673, Conditional κ = 0.001716140425997441: #2696's lender assignment with #2679's pre-life hosting and a window-optimal fill #2745, 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), mdumitrean (Improve conditional kappa to 0.00171625567823018 with composition and a frame refit #2733), Cinna Davis (Research: 80-helper anticipatory borrowing component and exact price rejection (no new kappa) #2226).
• Related: DavidAriasC (Improve conditional κ to 0.001717256973467 with credited routing-frame fusion #2766), jeremykothe2 (Conditional κ = 0.001717256973467002: post-cut partner correction on #2696's lender assignment with #2679's pre-life hosting #2767), Dugongue (T94 retained-tail allocation on PR2802: conditional kappa 0.001717795160032012107407 #2824, T104 paid allocation and exact prefix reserve: conditional κ ≈ 0.001717795222616587743198 #2827).
• Conflicts: both audited PRs' retained notices credit this author's PR1964 in the inherited lineage. This package
  reuses this author's own earlier checkers (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, 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, Independent verification (no κ): #2530's source-partner words exact through cleanup and endpoint; stock, endpoint enclosure and κ composition reproduce; no defect found #2804).

Prepared by Sagar Thakrar with substantial AI assistance (Claude Code, Anthropic, Claude Opus 5.5): AI scouts, three
independent AI auditors, AI builders and two rounds of AI review. No independent human review is claimed. Apache-2.0.

🤖 Generated with Claude Code