Construction: cap unfinished outputs in dirty fanout

research/bounded-pending-fanout-seed53/CLAIM.md

@@ -0,0 +1,148 @@
+# Cycle 7 local claim
+
+## Completed result, 2026-10-13 19:26 UTC
+
+Submitted [PR1168](https://github.com/CrocSwap/integer-mult-bounds/pull/1168),
+attached to the originating owner chat. This is the claim's one result update.
+The bounded-pending scheduler attains `2 sum c_A + 2 ceil(k/(2W)) c_B`.
+The cap-two fixture uses 404 primitive calls, compared with 716 for separate
+restoration and 300 with minimum pending capacity three. All four dirty rows
+restore. No new kappa, supplier or physical-memory improvement is claimed.
+
+Verification passes on CPython 3.11.15 and 3.14.8: 529 family cases, 46 complete
+child returns, 189 dense cases and inverses, five exact finite minima, 14
+negative controls, a nonlinear counterexample, five on-disk corruption controls,
+standalone optimized relocation and byte-identical certificate regeneration.
+Selected integrity and all 25 selected tests pass. A globally correct
+cross-boundary swap is rejected by the separate child-restoration check.
+
+The F3 line remains stopped as covered. No second pivot, selected-frontier
+edit or change to another contributor's PR was made. Full/cold supplier replay,
+Linux, formalization, hosted-CI success and independent human review are not
+claimed. The repository has neither codex nor codex-automation labels.
+
+## One evidence-driven pivot, 19:08 UTC
+
+The first-result overlap check found that all six PR1088 certificate words
+already have adjacent equal queries. Replacing `F^s F^s` by `F^(-s)` modulo
+three yields all six 13-query repairs directly. This is an existing-witness
+consequence and does not merit a new PR. The characteristic-three line stops.
+
+Replacement scope: an exact scheduler for PR889's one-source fanout under
+a cap W on unfinished outputs, with outputs committed permanently on their
+last query. Expected result is a complete query bill
+`2 sum_i c_Ai + 2 ceil(k/(2W)) c_B`, plus preparation, admission and dispatch.
+This is a new scheduling constraint and useful emitted tool; no new commutator
+identity, unconstrained optimum, physical memory saving or kappa is claimed.
+
+PR889 `e2021d1c9e06948528cbc0a8fd7079b671da981d` supplies the restored fanout
+and unrestricted `2k+2` minimum. PR938
+`df645942469e6a739ec94010a6068c398f4a6c86` characterizes every unrestricted
+minimum word. Its actual complete proof was read, including its plateau
+condition: equality permits splitting outputs around two B calls. The
+replacement must cover W below `ceil(k/2)`, where those equality words cannot
+meet the cap. The new lower bound uses live-output incidence at *every* B call,
+including longer words and arbitrary numbers of A calls. It is not another
+equality-word census. At k=5,W=2 the candidate needs four B calls; the
+unrestricted construction needs two but cannot meet that cap. The scheduler
+must also independently detect attempted early commits and cap violations.
+
+PR982 `5eca5b435d2ce172edf6ffb85694c7efa31bf114` and PR1103
+`92822cb99a7e1a28cb9d03ae5adb8e7988f30d1c` borrow outputs as connectors;
+the replacement keeps a dedicated connector and excludes all outputs from
+child scratch. All-state body searches for serial/online/committed/pending
+output scheduling found no competing scope. Recent issue comments and the
+no-pinned-issue result remain unchanged. No further pivot is permitted.
+
+Acceptance now requires an emitted capacity-respecting word, an all-k/W
+proof of the complete positive-price query optimum, exact free-map and dense
+commit checks, literal child lowering, paid recurrence and mathematical/package
+negative controls. The fixed seed fixture has five outputs, cap two, B length
+seven and A lengths two through six. Original cycle deadlines remain in force.
+
+The first complete replacement result passed at 19:14 UTC. The overlap refresh
+at 19:17 UTC covered 770 open PRs through #1155 and confirmed PR889/938/982/1103
+heads unchanged. New PR1155 `9821c6e9388f3fc097e94b72be9fa7b41a849527`
+coalesces read-free phase/permutation restorations. It changes a restoration
+operator family; it does not constrain pending fanout outputs or count query
+incidence. No competing capacity result was found. Verification/handoff began
+at 19:17 UTC, before the mandatory 19:27:24 UTC reserve deadline.
+
+The original selection record follows, preserved as a stopped investigation.
+
+Final pre-submission overlap check at 19:24 UTC covered 777 open PRs through
+#1162. New PR1158 `6336d879c0ba168463bf2f6fae9e653c870299fc` prices
+four-source Hadamard readouts with a fixed source-call class, without a
+pending-output cap; PR1159 `f38bfe5da0bed21f42ce5251d23491a56519d7c4`
+provides modular ancestor borrowing. Neither supplies this scheduler or its
+capacity lower bound. No same-scope claim or pinned sprint issue was found.
+Upstream advanced to `c0e3631dc24e3c24a861f7d3d79e0608481cccec`; its
+selection remains PR1094. The research base stays `ce7ad1b6...` as recorded.
+
+Claimed 2026-10-13 19:04 UTC by Sagar Thakrar, with substantial OpenAI Codex
+assistance. Owner chat `01a136a0-2a0e-7a71-853d-fef24da4b94d`, host `local`.
+OS-random assignment seed 53, recursive interfaces.
+
+Base `ce7ad1b6ab09452c3478723a2e96ed5ff212dc08`. Checkout
+`/Users/thakrarsagar-dev/Documents/Codex/2026-10-13/continue-the-user-s-research-loop-13/work/integer-mult-bounds`.
+Fetch completed 18:57:54 UTC. At 18:58:07 UTC clean local main and fetched
+origin/main both equaled that base; only then was the new branch
+`research/cycle07-seed53-recursive-interfaces` created. Earlier branches remain.
+
+Cycle starts 18:57:24 UTC; select by 19:05:24; begin verification by 19:27:24;
+finish by 19:37:24. No reset of these deadlines and at most one evidence-driven
+pivot. Expected deliverable is an exact characteristic-three connector
+construction, scoped optimum and complete recursive bill, with no new kappa.
+
+## Candidates and early overlap check
+
+1. Weighted repair of PR943's five-source binary obstruction. PR943 at
+   `cf360b4b09b7d0419decdd6ac85421fefed55bdd` already supplies the 945-path
+   census and both repairs; PR1083 at
+   `ae95248b3301e3fafe05c1c00020f69edcdceb98` formalizes its finite exclusion.
+   A cheap prefix-set check found singleton missing masks of weights three
+   and five. A weighted restatement follows from that existing census.
+   Rejected as insufficient new evidence; no expanded search will be claimed.
+2. Unequal positive/negative prices for PR1088's signed repairs. PR1088 at
+   `b0396aad724fec58630fbd4d13a809c562f18d9e` already supplies every repeated
+   operator. Each operator's balanced signs make pair-average pricing an
+   immediate reduction. Rejected as covered.
+3. Selected: characteristic-three restoration by three equal-signed calls,
+   on PR944's canonical three-by-three obstruction. PR944 at
+   `5dbcfbc63f646de5a1354f6b9760ec03837233f0` explicitly restricts its
+   14-query minimum to characteristic zero and excludes finite characteristic.
+   Its actual README, certificate, notice, and accepted ledger scope were read.
+   PR1088's six repairs also require characteristic-zero even multiplicities.
+   A small F3 check produced six 13-query occurrence profiles. This changes
+   the restoration algebra, rather than the seed or an existing query word.
+   New evidence will be six literal words, the sharp positive-price formula,
+   exact independent arbitrary-dirt replay, characteristic controls, and a
+   literal balanced child expansion. No physical supplier improvement follows.
+
+The first overlap scan read 1,140 all-state PR records through #1142, all open
+PR bodies, current review/ledger and recent issue comments. A fresh pinned-issue
+GraphQL query returned no coordination issue, so this claim is local. Targeted
+body searches for characteristic-three/F3/thirteen-query connector work found
+no same-scope result. PR1057/1135 cover exact-additive/rounded ancestor borrowing;
+PR1103 covers rectangular output borrowing. Their interfaces remain distinct.
+
+The selected certificate was followed to PR1094's source inventory, assembly
+and batch1099 review: conditional kappa `836330098538459/500000000000000000`,
+complex-binding, bit supplier PR589/555. Those files and upstream/ stay unchanged.
+
+## Scope and acceptance
+
+Only this new research directory changes. No existing callers, tests, fixtures,
+configs, exports, selected certificates or upstream files need edits. Inputs
+are distinct fixed ports; exact linear maps over characteristic three; signed
+unit additive queries; arbitrary initial dirt; no approximate leaves.
+
+Success requires literal 13-query witnesses for all six extra-call choices,
+a complete lower-bound reduction, independently checked recursive expansion,
+paid source access/restoration/control/storage, meaningful negative controls,
+source pins and an isolated reproducible command. No general circuit optimum,
+new supplier, larger kappa, formal proof or runtime speedup is promised.
+
+Stopping rule: complete this fixed six-witness obligation and its checks.
+Recheck overlap at the first concrete result and before publication. If it is
+covered, keep an honest local record rather than force a PR.