DONE: helper-donor kernel census on the #1297/#1305 words (#1337); pivot-566 follow-up (#1625)

[mdumitrean]

Status: DONE, claim released · updated 2026-10-14 23:17Z · priority revision 4 (main 0fdd7d82).

Question: which of the 306 early-read helper pivots on #1297's two words (also #1305's and #1319's) admit an exact helper-donor kernel that lowers the #1186 optimal frames? Changed premise: #1305/#1324 were withdrawn; the follow-up uses #1319's T74 hosting.

Result:

• Neither tested family (Conditional κ = 0.001676070884699375: exact helper-donor cold kernel for pivot 531 on the global mixed X54 fusions word #1274/Conditional kappa 0.001676854978651125: four composed helper-donor cold kernels #1297 two-shock relations, exact read re-timings) lowers the frames at any of the 306 pivots: #1337, author-checked.
• A seven-insert kernel outside those families does: pivot 566 on the same words, conditional κ 0.001676896669021299, +4.14e-8 over Conditional kappa 0.001676855229071321: verified exact fill on 74 replicas #1319 (#1625). Independently checked by philippeVV (review); not yet maintainer-reviewed.
• bbMisk's pivot-440 subtask: #1431 (merged).

Artifacts: #1337 at c9da5f27, #1625 at c7cac078 (branches on mdumitrean/integer-mult-bounds).

Next: maintainer review of #1625's inherited #1319 admission. For further kernels on the T74 words, see ianlibanio's handoff #2143 (interacting inserts, the extra word).

Claim: released.

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Original claim (2026-10-13), unchanged:

CLAIM (Marius-Paul Dumitrean, with substantial Claude (Anthropic) assistance). Expires 2026-10-14T00:45Z (extendable).

Question. #1274/#1286/#1297 replaced the early reads of four analogous cold pivots (531/543/555/567) with exact helper-donor kernels: a two-shock dyadic relation plus one tail correction, priced by the unchanged k8 frame model. #1297's final words are byte-identical to #1305's. In both of them, 306 helper pivots are still read before their first B write (with 1/2/3/4/5 early reads: 106/58/85/55/2 pivots; 72 are never written in B). Which of these admit an exact dyadic two-shock relation, which matches are legal and lower the exactly optimal frames, and how many compose?

Base / predecessors. main bce54fb3; #1297 4abf710a (rohanarun: search rule search_relations.py, words); #1305 a96a5d95 (jeremykothe2: idle overlay, strict package); #1274 (Jeremy Kothe: mechanism); #1186 (our exact frame harness).

Method / domain. First, #1297's relation rule, unchanged except that never-written pivots are included, run over all 306 pivots in both final words. Then every match is priced with exact optimal frames (tail-mutable, cone caps, cut equality) via the #1186 harness, after an exact program-map screen. Then the kernels are composed, re-priced jointly. The final words go through audit_local, a fresh native replay, and #1305's strict package with its owners, dispatch and idle-overlay code unchanged; the PLAN/SPEC are re-bound through its discovery path.

Expected artifact. Either a conditional κ above 0.001677162029073474 with full admission, or a scoped negative census: per-pivot match counts and exact prices. This is distinct from tomdif's block-kernel claim (#1167): it uses the unchanged #1274 two-shock family on new pivots. No selected-frontier change is proposed.

[mdumitrean]

DONE: #1337 (head abd7384d, base main bce54fb3). No new κ. Claim released.

FINDING. These results hold on #1297's two local words, which #1305 and the newer #1324 (0.001677380107853623) both use as identical blobs. Neither family improves the exactly optimal #1186 frames for any of the 306 early-read helper pivots:

• Conditional κ = 0.001676070884699375: exact helper-donor cold kernel for pivot 531 on the global mixed X54 fusions word #1274/Conditional kappa 0.001676854978651125: four composed helper-donor cold kernels #1297 two-shock helper-donor relations:
  • restoring at the end of early cleanup gives 61 candidates on 25 pivots: 32 neutral, 8 infeasible, 21 inexact;
  • restoring before the first write gives 292 candidates on 43 pivots: 52 neutral, 240 infeasible.
• Exact early-read re-timings: 803 moves, of which 635 are neutral and 168 infeasible.

Verdicts are unchanged at #1324's endpoint weights. A positive control reproduces #1297's 5+5 hooks for pivots 555/567 at −11,707 (H1 −3, H3 +1).

Idle. #1305's selection equals the exact optimum of its verifier's donor-star class in all 3,687 groups, and no size-4 group admits a three-receiver donor there. #1324's swap class is the larger class that does.

Validated locally:

• Conditional κ = 0.001677162029073474: four helper-donor cold kernels (pivots 531, 543, 555, 567) composed with multi-donor idle exchanges toward rank 51 #1305 verify.py: PASS 0.001677162029073474 (fresh native replays, 127 s).
• Conditional κ = 0.001677380107853623: idle rank-48 axis reassignments with simultaneous swaps toward rank 51 on #1305's four cold kernels #1324 verify.py: PASS 0.001677380107853623 (156 s).
• The Tooling: exact frame solver and delivery-rewrite search for gauge44/k8 local words (no new κ) #1186 pricer reproduces both κ values exactly.

HANDOFF. The uncompensated deletion screen ranks pivots 439/444 (−67,944), 438/440 (−62,316) and ten pivots at −51,648 (≈ +1.16e-6 κ if fully realized). It is a screen, not a bound: deleting 555/567 uncompensated is frame-infeasible, yet the kernels gain. Next step: extend census.py to window donors x += c·q … x −= c·q on any register, closing before q's first write. Then solve sparse dyadic combinations of at most three terms on those pivots and price them with price.py.

Prepared by Marius-Paul Dumitrean with substantial AI assistance (Anthropic Claude, via Claude Code).

[mdumitrean]

Correction + finding. #1305 and #1324, cited above as validated, were withdrawn by their author: the idle overlay changes Z4 family multipliers that the DATA-PHASES recipes fix. Their verify.py runs passed, but those verifiers do not check this rule, so the "Idle" and "Validated locally" lines are historical only. The census itself is unaffected. The current top open claims #1319 and #1377 use #1297's words byte-identically (blobs eacf8c77 and 4d464f55). At #1319's complex lower endpoint the positive control re-prices at −11,705.

On #1431's control. We priced bbMisk's four-window repair for pivot 440 with the #1186 exact frame harness, on both #1297 words at #1319's endpoint. The repair is exact: the pivot's column over B and early cleanup checks in exact fractions. It is frame-infeasible: an early-cleanup vertex fails L ⊆ U. The deletion is not the cause. Deleting the three reads alone is frame-feasible (−62,300, uncompensated). Each of the four windows is infeasible on its own, even inserted into the unchanged word. So in this model the obstruction comes from reading 440 at those B positions (41, 160, 493, 527). A useful pre-screen for further window searches is the frame feasibility of single inserted reads by position.

Prepared by Marius-Paul Dumitrean with substantial AI assistance (Anthropic Claude, via Claude Code).

[bbMisk]

DONE — PR1431, head 764d1334b7e0d135a25baff029018fad20e581da. Scope released.

The scalar repair minimum is exactly four windows for pivot 440 of the pinned PR1297 BASE-WORD, when each restored donor window spans at most four consecutive reads inside a no-write segment. The proof strengthens the originally claimed six-coefficient scan to arbitrary rational coefficients (and hence complex coefficients for these rational systems). It covers 2,758 windows, one with zero response, and 1,611 projective directions. A separate direct-pulse / integer-rank checker covers 5,177,758 cases. Four explicit windows restore all 704 arbitrary input columns, but add eight ADD macros and have no physical frame or paid-moment admission.

Reproduce: python3.12 -B scripts/research_package.py --package research/complex-p440-window-shocks. Registered Python 3.12.13 replay, seven test groups, isolated optimized read-only Python 3.14.6 relocation, source pins, Ruff and selected-record integrity pass. No new kappa, full cold replay, native/hosted admission, Lean or independent human review is claimed.

This is a bounded extension of PR1337's open handoff, not an exclusion of unrestricted windows or other pivots. Exact sources, proof, costs, controls and remaining questions are in the package. Credit Marius-Paul Dumitrean / PR1337, Rohan Arun / PR1297, Jeremy Kothe / PR1274 and the retained lineage. Hanson Sun (@bbMisk), substantial OpenAI Codex assistance, Apache-2.0.

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Original claim (retained for scope history):

CLAIM — complex supplier; OS assignment seed 34.

Base: bce54fb3f895cbe5cd4c0eb477c3afeed100190f. Predecessor: PR1337 abd7384d9a5e35048723512ae70d970909ffd522 (exact fetched head will be retained in the package).

I am taking one bounded part of the three-shock/window-donor handoff: pivot 440 of the pinned BASE-WORD. Seed 34 selects index 2 of the sorted high-screen pivots [438,439,440,444]. Delete its three early B reads, then test up to three restored donor windows on any nonpivot source register. Each window spans at most four consecutive source reads inside one no-write interval before the pivot's first write. Coefficients are {-2,-1,-1/2,1/2,1,2}. This enlarges the old output-reader-only two-shock family; other pivots and arbitrary coefficients are excluded.

Method: exact suffix responses, support-guided / modular rejection with exact rational confirmation of any match, then complete frame/cost pricing if a candidate survives. All donor entry/exit additions and restoration are charged. Deliverable: a reproducible finite census with meaningful controls, or one checked candidate and explicitly unresolved admission obligations. No new kappa is promised. Expected finish 2026-10-14 01:20 UTC; claim expires 02:25 UTC.

Credit Marius-Paul Dumitrean / PR1337, Rohan Arun / PR1297, Jeremy Kothe / PR1274 and the retained lineage. Hanson Sun (@bbMisk), with substantial OpenAI Codex assistance.

[mdumitrean]

DONE (follow-up to the handoff above): #1625. Head 62092e96, stacked on #1319's head 603defe5.

Conditional κ = 0.001676896669021299, +4.144e-8 over #1319's unchanged construction. Stacked with #1549's 200-digit refinement (its assembler vendored unchanged, with this construction's own 1e-200 certified endpoints), the value is 0.00167689666902129930775071099726796…, 4.144e-8 above #1549 and the later digit refinements.

FINDING. A seven-insert helper-donor kernel for cold pivot 566 on #1297's two words (as vendored in #1319):

• delete B755 (494 -= q);
• a helper window on 98, restored in the early cleanup right after q's own restoration;
• donor windows on 590 and 672;
• direct reads 150 += q and 209 -= q.

It is exact on the full B + early-cleanup map, and per call it changes H1 +1, H2 −2, H3 +1 on both words (−1,855). #1319's owners, dispatch, parent and idle remainder are unchanged. After a provider-only PLAN rebind, #1319's strict T74 replay passes: 114 admission, 12 bit, 8 owner, 6 geometry and 4 outer controls rejected, and all 47 outer margins positive. The kernel lies outside the two-shock family searched in #1337/#1338.

Reproduce:

• bounded: python3.12 scripts/research_package.py --package research/t74-pivot566-kernel;
• full chain: research/t74-pivot566-kernel/replay_full.py --refined.

Open next questions are in the package.

Prepared by Marius-Paul Dumitrean with substantial AI assistance (Anthropic Claude, via Claude Code).