Cancel cleanup sandwiches of 99 helpers on #272: conditional κ = 7.1366215638961e-4

[evmckinney9]

Based on main at 3b6b668, with #272 (Dugongue) at 4d23d0ee as the pinned base. It adds research/cleanup-sandwich-272/ and one workflow; no existing file changes. #272's package is not copied. verify.py takes it as --base, checks its manifest against SOURCE.json, runs #272's own verify.py first, and then reuses #272's compiled native checkers. The workflow fetches the pinned commit.

Under the interfaces retained by #272, this package certifies

T(n) = O(n (log n)^(1 - κ)),   κ = 713662156389609974540991/10^27 = 7.13662156389610e-4

That is +0.223% over #272 (7.12074434532274e-4).

Change and mathematical scope

Idea. Some helpers climb to the full frame only to take part in cleanup. When that part is redundant, the climb can be removed. Here the redundancy is the F2 identity t += a; a += b; t += a = a += b; t += b. As a result, 99 helpers in #272's word stop at dimension 4 instead of 24. Each saves two rank-21 climbs, and its banked endpoint shrinks from rank 23 to rank 3.

After #272's first kernel cut, 99 helpers appear in exactly three gates, all in the full-frame cleanup:

t += a,   a += b,   t += a        (F2)

with t never a control between the first and the last. The rewrite moves a += b to the cut. There a and b already sit at frames whose sum is a nondegenerate four-dimensional frame. t += b stays at the middle gate's position and frame. Each such helper then has no gate after the cut. Its completed endpoint becomes the rank-3 partial swap D_(P_F − P_S), by the completed-core identity of #186 and research/community-round8-audit/BANK-SCHEDULE.md.

	normalized stock	coarse bit saving	κ
#272	519,887	712581842140497/10^18	712074434532274423885827/10^27
this PR	517,907	714171830081841/10^18	713662156389609974540991/10^27

• Histogram: per helper, two rank-21 steps are removed, and two rank-1 steps and one rank-20 step are added (rank mass −20).
• Banks: over Frame-filtered collective kernels + target-prefix sharing: kappa = 0.000712074434532274423885827 #272's 120 replicas, the banks re-tile exactly with 1,980 fewer banks per stage.
• Re-tiling: Frame-filtered collective kernels + target-prefix sharing: kappa = 0.000712074434532274423885827 #272's own bank review charges every role as if its chain ended at full, so this package does the re-tiling for the shorter chains and checks it exactly.
• Binding: the deficit is unchanged, and the bit supplier still binds.

PROOF.md gives the argument and scope.

Assumptions: every all-size interface #272 retains (compiler, common weighted chart, restored rows, routing, prime supply, precision and recovery, analytic reduction) stays an assumption.

Not claimed: that 99 is the largest such set.

Validation

python3 -m pip install sympy==1.14.0
git fetch https://github.com/CrocSwap/integer-mult-bounds 4d23d0ee5682c99b792614bae4bc5330da19ff13
git archive 4d23d0ee5682c99b792614bae4bc5330da19ff13 research/filtered-kernel-target120 | tar -x -C /tmp/base272
python3 -B research/cleanup-sandwich-272/verify.py --base /tmp/base272/research/filtered-kernel-target120 \
    --boost-include /usr/include --output /tmp/cleanup-sandwich-272

verify.py runs these checks in order:

1. Base pins.
2. Frame-filtered collective kernels + target-prefix sharing: kappa = 0.000712074434532274423885827 #272's own full replay.
3. The 99 frozen sandwiches: nondegenerate new frames for 9I − J, and exact rational inclusion of every new connector.
4. The F2 replay of all 20,107 formal source, target and dirty columns, with both omission controls rejected.
5. Frame-filtered collective kernels + target-prefix sharing: kappa = 0.000712074434532274423885827 #272's native legality, prefix-kernel, bank-chart and five-stage-column checkers, unchanged.
6. Rank-3 endpoints with exact charts, and the exact bank re-tiling.
7. Normalizer charts.
8. Frame-filtered collective kernels + target-prefix sharing: kappa = 0.000712074434532274423885827 #272's price engine (47 constraints, adjacent grid point rejected), finite invoice and fixed-prime refinement.
9. Equality with expected.json.

Checks run on this branch (Linux x86-64, Python 3.12, g++, SymPy 1.14.0):

• Full verify.py: run from a fresh git archive of 4d23d0ee. Result: PASS.
• make entrance-bank-verify: PASS.
• -O guard: python -O verify.py refuses to run.

Credits

• Dugongue: Frame-filtered collective kernels + target-prefix sharing: kappa = 0.000712074434532274423885827 #272, the pinned base word and package; Multi-cut kernel condensation: 518 entrances, kappa = 7.11029386054035e-4 #259 multi-cut kernel condensation; Response-kernel entrance gauges: 132 helper-pair rewrites, κ = 7.1046520063283e-4 #254.
• rohanarun (Rohan Arun): Conditional κ = 7.11032238200698e-4: concave-descent frame retiming of 25 gates on #259's multi-cut condensation #263 concave-descent retiming.
• eumemic: κ = 7.10392186446856e-4: transport dirty compensations to 21 entrance frames #249 transported entrances and the source527 five-stage construction.
• Douglas Colkitt: the completed-core bank scheduling supplement.
• Everyone credited in Frame-filtered collective kernels + target-prefix sharing: kappa = 0.000712074434532274423885827 #272's NOTICE.md.

The construction was found with OpenAI Codex (GPT-6 Astra) assistance; the package and its independent replay were prepared with Anthropic Claude assistance. No priority over concurrent work is claimed.

[evmckinney9]

Retargeted from #263 to #272 (Dugongue, 4d23d0ee), the current frontier in this lineage. On #272's word, the same three-gate cancellation applies to 99 helpers (45 on #263). The package now runs #272's own verifier and its compiled native checkers on the rewritten word, then reprices with #272's engine, finite invoice and fixed-prime refinement: κ = 713662156389609974540991/10^27 = 7.13662156389610e-4, +0.223% over #272. A from-scratch replay from a fresh git archive of 4d23d0ee passes all eight checks. The new commit moves the package to research/cleanup-sandwich-272/; the title and description are updated.

[evmckinney9]

Follow-up notes for review.

CI. Upstream workflow runs on this PR wait for maintainer approval. The package's own workflow passes on the fork at ebc1def on both matrix entries: run 38022674843, Python 3.11 in 348 s and 3.14 in 488 s. Each job fetches #272 at 4d23d0ee, runs #272's full verifier, then this package's checks.

Composition with neighbouring PRs. The three-gate identity does not depend on the base, but the set of helpers that carry the sandwich t += a; a += b; t += a does. I ran the same selection on each word with no other change:

base	κ of base	helpers with the sandwich	shared with #272's 99
#263	7.110322e-4	45	16
#272	7.120744e-4	99	99
#273	7.119490e-4	45 (the same 45 as on #263)	16

• Conditional κ = 7.11948953756315e-4: target-prefix compression (209 square groups) composed with the multi-cut kernel condensation #273 is disjoint from this rewrite. Its supplementary pivot families and target-prefix compression leave all 45 of Conditional κ = 7.11032238200698e-4: concave-descent frame retiming of 25 gates on #259's multi-cut condensation #263's sandwiches unchanged, so it composes with the rewrite without conflict.
• Frame-filtered collective kernels + target-prefix sharing: kappa = 0.000712074434532274423885827 #272 changes the cleanup suffix. Its frame-filtered kernels add 83 sandwiches and remove 29, which is why Frame-filtered collective kernels + target-prefix sharing: kappa = 0.000712074434532274423885827 #272 is the stronger base here. On Conditional κ = 7.11948953756315e-4: target-prefix compression (209 square groups) composed with the multi-cut kernel condensation #273, the rewrite would give about +0.10% (estimate, not certified), below this PR.
• Rebasing. If a later base in this lineage overtakes Frame-filtered collective kernels + target-prefix sharing: kappa = 0.000712074434532274423885827 #272, selection.json, SOURCE.json and expected.json have to be regenerated for it; the code does not change. On Conditional κ = 7.11032238200698e-4: concave-descent frame retiming of 25 gates on #259's multi-cut condensation #263 and Frame-filtered collective kernels + target-prefix sharing: kappa = 0.000712074434532274423885827 #272, the selection and rewrite took under a minute.

Independent agreement. Two separately written pipelines found and checked this construction: the search-side scripts that first located the 45 helpers on #259/#263, and this package. Their receipts on #263 agreed byte for byte except for timings and paths.

[Mister-Meeseeks]

Thank you @evmckinney9. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Cleanup-sandwich cancellation for 99 helpers.

Review and limits: Fresh full exact-parent and changed-word replay passed in 321s: all 99 helpers, 20107 formal columns, 198 rejected gate omissions, native legality/prefix/bank/global checks, exact endpoints/normalizers and fixed-prime pricing.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: ebc1defe8c13f39f86e5901c3437c1be52886a2b. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.