Independent verification: #2802's seven-stage increment over #2751 (retired5 + retired7 stages) passes 28/28 rules and 20/20 controls; covers #2818's identical construction (no κ)

[thakrarsagar]

Label: Independent verification (no κ). Milestone: audit. No defect found. No selected frontier is changed and no κ is claimed.

What this decides

Fresh standard-library code checks the construction behind PR #2802 (mdumitrean, head 17b2ee6e): its seven declared stages, which turn PR #2751's two T74 BORROW-WORDs (tekuuu, head 4cfbb0cc) into the words with git blobs 91bd9c68f209… (base) and 6c4a9a4395cf… (extra), plus the FILL2751 → FILL transform. The new construction is separated from #2751 and PR #2766, as the maintainer's T74 reviews ask (community-efficient1000, #1992 row: "separate the actual new construction from inherited ancestors").

1. The word construction passes: 28/28 named rules on both words, and all 20 negative controls are rejected by their named rules. Seven pending claims build on these words (PR heads and blob identities read from the GitHub PR file lists at 02:10 UTC; all heads re-checked unchanged at 02:16 UTC; this list is dated and not part of the verifier):
   • Conditional κ ≈ 0.001717794984118634663827: two hostee moves and seven retired-lender aliases on #2751's joint twelve-source words #2802 and Conditional κ = 0.0017177949841186346638272: #2802's construction with a 1e-3000 certified endpoint #2818 ship these words unchanged. Conditional κ = 0.0017177949841186346638272: #2802's construction with a 1e-3000 certified endpoint #2818 (jeremykothe2, head 175822ae) has byte-identical words, fill, ORDER and providers, so the verdict covers its construction.
   • T94 retained-tail allocation on PR2802: conditional kappa 0.001717795160032012107407 #2824, T104 paid allocation and exact prefix reserve: conditional κ ≈ 0.001717795222616587743198 #2827 and Tensor block norm accounting: T114 raises conditional kappa by 5.160482894338e-11 #2839 (Dugongue) vendor these words and Conditional κ ≈ 0.001717794984118634663827: two hostee moves and seven retired-lender aliases on #2751's joint twelve-source words #2802's fill (6441c0be…).
   • Conditional κ = 0.001718657437166855: dirt-entry rewrite of helpers 530 and 542 on #2802's construction #2833 (jeremykothe2) uses Conditional κ = 0.0017177949841186346638272: #2802's construction with a 1e-3000 certified endpoint #2818's retired7_43{base,extra}.json patch blobs unchanged, and T124 integer-prefix composition on PR2833: conditional κ ≈ 0.00171865827784172 #2843 (mdumitrean) builds on Conditional κ = 0.001718657437166855: dirt-entry rewrite of helpers 530 and 542 on #2802's construction #2833.
2. Neither of Conditional κ ≈ 0.001717794984118634663827: two hostee moves and seven retired-lender aliases on #2751's joint twelve-source words #2802's two changed acceptance checks is an acceptance gap for κ.
   • R is bound to the words. R = 408 is derived here from the words, not from the providers, and Conditional κ ≈ 0.001717794984118634663827: two hostee moves and seven retired-lender aliases on #2751's joint twelve-source words #2802's own compact() check and the inherited ENTRANCE-WIDTH-BINDING stage already tie it to them.
   • Alias occupancy holds for the shipped words. No check on the model's pricing path reads it, so in the finite model it is a conformance property, not a soundness condition for κ (details below).
3. Not covered: the later stages of T94 retained-tail allocation on PR2802: conditional kappa 0.001717795160032012107407 #2824, T104 paid allocation and exact prefix reserve: conditional κ ≈ 0.001717795222616587743198 #2827, Conditional κ = 0.001718657437166855: dirt-entry rewrite of helpers 530 and 542 on #2802's construction #2833, Tensor block norm accounting: T114 raises conditional kappa by 5.160482894338e-11 #2839 and T124 integer-prefix composition on PR2833: conditional κ ≈ 0.00171865827784172 #2843 (allocations, fills, reserves, dirtentry, block-norm accounting, T124); Conditional κ = 0.0017177949841186346638272: #2802's construction with a 1e-3000 certified endpoint #2818's 10⁻³⁰⁰⁰ endpoint; native lowering; the T74/Conditional kappa 0.001676855229071321: verified exact fill on 74 replicas #1319 supplier admission; the PR1673 outer proof. A pass is necessary but not sufficient for any of these claims.

Reproduce

From the repository root, with git and Python (standard library only):

python3 -I -B research/t74-retired7-increment-audit/verify.py --fetch

Expected last line (about 2 minutes, under 0.6 GB RSS):

PASS_T74_RETIRED7_INCREMENT_AUDIT rules=28/28 controls=20/20 commit2802=17b2ee6ef3cf commit2818=175822aee7a1

--fetch downloads refs/pull/{2802,2751,2818,2766}/head only if a pinned commit is absent, and writes only FETCH_HEAD. Every input is checked against a sha256 pin. --out RECEIPT.json rewrites the deterministic receipt shipped in the package; reruns are byte-identical.

Python versions. Only Python 3.14 was run. VERIFY.json registers the same argv for scripts/research_package.py, whose hook pins Python 3.12; that hook was not replayed locally, because only 3.14 is installed. --check-only metadata validation passes.

Base and pins

• Base commit 544a7e82810e30cab61c297cb2e2ea86127fe944 (priority revision 5). origin/main has since moved to d3597057. None of its changes touch this package, so the branch was not rebased.
• PR heads: Conditional κ ≈ 0.001717794984118634663827: two hostee moves and seven retired-lender aliases on #2751's joint twelve-source words #2802 17b2ee6ef3cf1468e78a6267f0ecbc9a0e6f60dd, Conditional kappa ≈ 0.00171714158635 via joint twelve-source recovery #2751 4cfbb0cc8314d7fb4e8e754545a49a42eb590a69, Conditional κ = 0.0017177949841186346638272: #2802's construction with a 1e-3000 certified endpoint #2818 175822aee7a1858ec653f7f92d7a750aec2c2795, Improve conditional κ to 0.001717256973467 with credited routing-frame fusion #2766 e6df920cd0110e4b629e2ad84eddcb539001e174. The 48 input blobs are pinned by sha256 in increment_audit.py (PINS).
• PR code was read only as pinned data. It was never imported or executed.

What is checked (both words)

• S1 event diff. Every difference between W2751 and W2802 is a declared stage edit:
  • 63 B relabels (35 alias5, 14 hostmove2, 14 alias7) at exactly the declared positions;
  • 62 frame changes (26 refit5, 32 refit5c, 2 refit7, 2 refit7c);
  • warps 30/31 replaced in place and warps 66–72 appended;
  • everything else unchanged.
• S2 occupancy timeline. 704 register segments (632 live + 72 warps; parent 639 + 65), each exactly one parent role. Lenders 550–553/562 retire in B (B901–B910). Only 401/403 retire in A (A3175/A3174), before warps 71/72 at B259/B262. The moved hostees enter 564/565 at B941/B944, after those lenders' last events at B911/B912.
• S2 replay. An exact free-algebra replay over ℚ⟨free group⟩ passes forward and dual, with 632 dirty inputs and 72 zero buffers. The re-derived 4,547-item cleanup equals the shipped one. A second method, random invertible 4×4 matrices over GF(2⁶¹−1) for 2 seeds, also passes.
• S3 frames. For 72 B warps and 24 prelude warp items: G is invertible, G(U) = E, G⁻ᵀ(U^⊥) = E^⊥, and K_G maps L_U onto L_E, with U the lender's actual propagated frame. Refit frames at the propagated floor: refit5 26/26, refit7 2/2, refit7c 2/2, refit5c 25/32. The 7 above-floor refit5c frames are cost-neutral: lowering any one of them, or all seven, leaves the profile unchanged.
• S4 profile. The local profile {1:2382,2:648,3:268,4:128,5:26,8:8} (mass 5188) and the inventory {4:26,5:2,7:62,8:78,9:240} (408 helpers) are confirmed by two subspace representations.
• S5 fill with word-derived R. R = 408. The fill has 271,728 = 666 × 408 roles in 1,332 windows, idle {1:17316,3:6594,5:9878,32:1,48:26558}. It equals FILL2751 minus exactly the 4,662 roles of the seven followers.
• S6 price (repeat check). Complete profile mass 4,816,512. f(C) < 66,304 < f(C + 10⁻²⁴) for C = 0.001717794984118634663827. The evaluation is at 80 digits with a written error budget and a 10⁻⁷⁰ widening; the minimum bracket margin is 1.046×10⁻²⁰. Exact margins over Conditional kappa ≈ 0.00171714158635 via joint twelve-source recovery #2751, 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.
• Positive control. The same code reproduces Conditional kappa ≈ 0.00171714158635 via joint twelve-source recovery #2751's profile, replays, fill (R = 415, 276,390 roles) and claimed complete profile.

Separating the new construction from its ancestors. This independently reproduces the split #2802 itself states and records in evidence/retired5/:

step	endpoint C	gain
PR2766	0.001717256973467002308270	—
retired5 stages (refit5, alias5, refit5c)	0.001717409316335491643448	+1.523×10⁻⁷ over PR2766
retired7 stages (refit7, hostmove2, alias7, refit7c)	0.001717794984118634663827	+385667783143020379/10²⁴ ≈ 3.857×10⁻⁷ over retired5

The reconstructed retired5 fill reproduces #2802's recorded fill_sha256 3501f6bd…. If the local zlib differs, a canonical-JSON pin is used instead and a NOTE: line says so.

Provenance correction. #2802 credits 20 frames to PR2766. PR2766's own pinned word changes only B1151. The other 19 (A0–A11, B771/773/776/778/783/788, restore60) are #2802's own refit5c choices and are cost-neutral (rule ATTRIBUTION-PR2766-WORD).

Alias occupancy (the replaced control for lenders retiring in A)

For alias7, #2802 replaced the control "warp before lender retirement" with "warp after the follower's first gate". No shipped control moves 401's or 403's own event past its alias warp, so the package builds such mutants:

• C4a/C4c move a dead last write into B after the alias warp, at the lender's own frame. Both scalar replays accept them; the frame chain rejects them (frame not monotone).
• C4d/C4e move a dead last write (one after the lender's last read) to the end of restore at frame FULL. Both replays, the frame chain, the recount, the refits, the fill and the price all accept them, with the profile unchanged. Only OCC-TIMELINE rejects them (plus S1-DIFF and X-2818, as undeclared edits).
• C4f/C4g move a lender read, or a write the lender still reads, the same way. Both replays reject them.

Consequences:

• No rule on the model's pricing path reads occupancy: not our replays, frame chain, recount, fill or price, and not the pinned PR2679 auditor (read, not run). In the finite model, occupancy is therefore a conformance property, not a soundness condition for κ.
• C4d passes because the moved write is dead. Follower 667 borrows the register dirty, and the re-derived inverse-reverse cleanup undoes the moved write first. These controls are examples, not a classification of all violations.
• Conditional κ ≈ 0.001717794984118634663827: two hostee moves and seven retired-lender aliases on #2751's joint twelve-source words #2802's verify_retired7.py enforces occupancy structurally (read, not run): A and restore are unchanged through all stages, and the declared stages must rebuild the word. Conditional κ = 0.0017177949841186346638272: #2802's construction with a 1e-3000 certified endpoint #2818's rebuild_borrow.py retired7 patch check has no occupancy predicate, but its words are byte-identical, so OCC-TIMELINE establishes occupancy for them.
• What is missing is at most an optional regression control. It is not needed for κ in the finite model.
• Unchecked: whether any layer outside the finite model (native lowering, physical hosting) relies on occupancy. The package checks only the binary-symplectic conditions of PR2226 §1's Clifford identity, not the operator-level identity.

Negative controls (20)

Each control counts only if its named rule rejects it. Seven controls also carry must_accept/exact_failing expectations, all of which are met. No rule crashes.

• C1 undo refit7.
• C2 revert the hostee move.
• C3 place warp 66 early.
• C4a–C4g the occupancy controls above.
• C5 warp 71 after the follower.
• C6 wrong G.
• C7 a consistent (U′, G(U′)) pair with U′ not the propagated frame.
• C8 keep follower 667 live: words say 409, providers and fill say 408.
• C9 swap the lenders (declaration conformance).
• C10 drop a restore gate.
• C11 fill inflated to R + 1.
• C12 hostee gate left on the old lender.
• C13 undeclared frame raise.
• C14 Conditional κ = 0.0017177949841186346638272: #2802's construction with a 1e-3000 certified endpoint #2818 word altered by one sign.

The full table, with the recorded reason for each, is in the README and RECEIPT.json.

Scope, assumptions and unresolved obligations

• Model. The finite BORROW-WORD model of PR2226 PROOF.md and the PR2679/PR2751 lineage is taken as the specification and is not validated here.
• Not re-derived. Conditional kappa ≈ 0.00171714158635 via joint twelve-source recovery #2751's twelve-source recovery, its 4(H8−H7−H1) delta and the PR2720 reconciliation. A sibling session claimed these in Cost-aware source-partner helper assignments above PR2588 #2612. W2751 is a pinned parent, and Conditional κ ≈ 0.001717794984118634663827: two hostee moves and seven retired-lender aliases on #2751's joint twelve-source words #2802's copies were checked byte-identical to Conditional kappa ≈ 0.00171714158635 via joint twelve-source recovery #2751's own files.
• Author-recorded in Conditional κ ≈ 0.001717794984118634663827: two hostee moves and seven retired-lender aliases on #2751's joint twelve-source words #2802's release; not independently re-checked:
  • native lowering and Clifford recipes for the new warps 30, 31 and 66–72;
  • the strict-t74 record. It carries the supplier-only κ 0.001714849224721887 under the older outer witness, not the claimed κ;
  • the modern outer arithmetic that yields C.
• Inherited and open.
  • The T74/Conditional kappa 0.001676855229071321: verified exact fill on 74 replicas #1319 supplier admission and the PR1673 capped phase-cell fusion outer.
  • Conditional κ ≈ 0.001717794984118634663827: two hostee moves and seven retired-lender aliases on #2751's joint twelve-source words #2802's own listed scope items: the all-size compiler, hosting, precision/tape, exact recovery, analytic transfer, the PR559 correction and the PR589 assumptions.
  • The "at most two aliases" census and philippeVV's 670/671 note.
  • Conditional κ = 0.0017177949841186346638272: #2802's construction with a 1e-3000 certified endpoint #2818's 10⁻³⁰⁰⁰ endpoint.
• Claim strength. This is a finite exact check of one construction, not a proof of the multiplication theorem. A pass removes no inherited obligation.
• Search record. No search was run. All checks are finite and exact on fixed pinned inputs. The matrix-realisation seeds are fixed at 1 and 2.

Open next questions

1. Does any layer outside the finite model (native lowering, physical hosting) rely on alias occupancy?
2. Is the whole refit frame assignment optimal under the moment cost? A better assignment could only raise κ.
3. Do the new warps 30, 31 and 66–72 have exact native Clifford/Gaussian lifts in both orientations?

Credit and what this adds

• Checked work.
  • Marius-Paul Dumitrean (@mdumitrean), Conditional κ ≈ 0.001717794984118634663827: two hostee moves and seven retired-lender aliases on #2751's joint twelve-source words #2802: the retired5 and retired7 stages and the recorded retired5 evidence.
  • Jeremy Kothe (@jeremykothe2), Conditional κ = 0.0017177949841186346638272: #2802's construction with a 1e-3000 certified endpoint #2818: concurrent repackaging of Conditional κ ≈ 0.001717794984118634663827: two hostee moves and seven retired-lender aliases on #2751's joint twelve-source words #2802 with a finer endpoint. Also Conditional κ = 0.001717256973467002: post-cut partner correction on #2696's lender assignment with #2679's pre-life hosting #2767 and the 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 lineage.
  • Tekalign (@tekuuu), Conditional kappa ≈ 0.00171714158635 via joint twelve-source recovery #2751: the parent words and fill.
  • Philippe Van Velzen (@philippeVV), Conditional κ = 0.0017148565406944334: pre-life hosting and a frame-refit alias on the #2588 T74 words #2679/Conditional κ = 0.0017044322370702051: owner-fill evacuation and two more retired-lender aliases on the #2526 T74 words #2559: retired-lender aliases and pre-life hostings.
  • Cinna Davis, Research: 80-helper anticipatory borrowing component and exact price rejection (no new kappa) #2226: anticipatory dirty borrowing.
  • Mason Hale, Improve conditional kappa to 0.001715599770234969498857 with concentrated source-partner assignments #2696: the eight-lender assignment.
  • @DavidAriasC, Improve conditional κ to 0.001717256973467 with credited routing-frame fusion #2766: the B1151 refit.
  • Vlado-V, Improve conditional κ to 0.001697060296258836 with coherent handoffs and retimed hosting #2322.
  • zxv, Conditional κ ≈ 0.0017137379215475043 from source-partner lifetimes and physical rehosting #2530.
• Downstream claims. Dugongue (T94 retained-tail allocation on PR2802: conditional kappa 0.001717795160032012107407 #2824, T104 paid allocation and exact prefix reserve: conditional κ ≈ 0.001717795222616587743198 #2827, Tensor block norm accounting: T114 raises conditional kappa by 5.160482894338e-11 #2839), jeremykothe2 (Conditional κ = 0.001718657437166855: dirt-entry rewrite of helpers 530 and 542 on #2802's construction #2833) and mdumitrean (T124 integer-prefix composition on PR2833: conditional κ ≈ 0.00171865827784172 #2843).
• Related prior audits. commdata2338's Research: independently audit PR #2588's swapped-alias frame bill and lender handoffs #2656. This account's merged 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 was the semantic reference for the model; no code was copied. Sibling PR 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 (same account) audits Conditional κ ≈ 0.0017137379215475043 from source-partner lifetimes and physical rehosting #2530's words and the Conditional κ = 0.0017148565406944334: pre-life hosting and a frame-refit alias on the #2588 T74 words #2679 order/windows.
• What this adds. Before this, nobody had checked Conditional κ ≈ 0.001717794984118634663827: two hostee moves and seven retired-lender aliases on #2751's joint twelve-source words #2802's stages, the occupancy of lenders that retire in A, or the word-derived R. Conditional κ = 0.0017177949841186346638272: #2802's construction with a 1e-3000 certified endpoint #2818 replays inside its own lineage verifier, which is not independent. This package provides fresh code for all three, together with a provenance correction for the 20 frames credited to PR2766.

Sprint, claim and review provenance

• Sprint. Track 60–74 (adversarial mathematical audit), OS-random seed 71.

• Claim. Start here: coordinating human and agent research #1163 (comment). Canonical thread: Cost-aware source-partner helper assignments above PR2588 #2612.

• Review. The package was reviewed by seven independent AI review passes in the same loop, and revised after each round. Round 1 had four passes (reproducibility, mathematics, provenance, referee). Round 2 had three (mathematics, reproducibility, referee). The round-1 fixes include:

  • correcting an overstated occupancy claim;
  • correcting the PR2766 frame provenance;
  • applying the root-bracket widening at a precision where it takes effect.

  The README lists every change. No human has checked the findings by hand.

Attribution and AI assistance

Prepared by @thakrarsagar with substantial AI assistance from Claude (Anthropic, Claude Opus 5.5) via Claude Code, in an automated research-sprint loop. Claude wrote and ran the code and these notes. Apache-2.0.

🤖 Generated with Claude Code