Certify two neutral-first retiming domains on the pinned staged544 providers

[Clear1nsight]

Change and mathematical scope

Continue #3886's explicit neutral-first two-edit question on both literal PR3734 staged544 providers. Every candidate in two declared domains has nonnegative new-minus-old raw moment for every real 0<a<1. No new supplier, kappa or selected-frontier change.

Per provider: 122 neutral frame-changing starts at displacement <=2 expose 1,035,911 interacting second prices. Of 3,928 adjacent commuting ADD pairs, 176 fail frame legality; the 3,752 legal neutral swaps expose 3,155,468 swapped-gate second prices and 1,045,449 third-gate new-middle-cut prices. A written exact reduction maps other third-gate destinations to baseline prices. The union uses the same 19 sign-certified delta types; there is no global obstruction claim.

All 122 frame-changing first words per provider pass the retained 723-input free-operator interpreter with 632 independent live inputs and 91 arbitrary dirty buffers, both orientations, reverse pull-back and cleanup boundary. Every adjacent first pair also passes a separate rational dirty-block matrix check. Thirty-nine coverage cross-checks per provider compare incremental traces and optimized reach tests with fresh full scans and the retained auditor. Eight rejection/sensitivity controls per provider pass.

The positive fixture decomposes the already-retained Jeremy Kothe #2957 recovery into a neutral first swap and profitable second frame edit, 2+3 -> 1+4. It recovers the pinned source and is a control, not a new improvement. The local ledger is 3,519 children and rank mass 5,134 per call, with unchanged 408 helper roles and 91 dirty buffers. Unknown physical/native/precision/supplier costs remain explicit in LEDGER.json.

Validation

Full standalone normal runs:

python3 -B research/staged544-neutral-two-edit/verify.py --provider base
python3 -B research/staged544-neutral-two-edit/verify.py --provider extra

Normal full replay passed on Python 3.12.3. VALIDATION.json records runtimes and the assertion-disabled controls. The registered compositional-dirty mode proves every first edit by exact local block equality plus full baseline replay and repeats every census, ledger and failure control. Full per-first interpreter replay remains available without that flag. The official registered replay and metadata/pin check pass against authenticated canonical Git objects in an explicitly shallow local fixture; delivered scientific code and replay-manifest bytes equal that checked snapshot. Full source-history preflight was not run locally. Hosted execution status is tracked separately below.

Scope, overlap and credit

Canonical base 20ecf28, priority revision 6. Task scalar-to-moment, with changed scope explicitly assigned by the user: continue #3886 beyond its frozen single-ADD certificate by permitting neutral first-word changes. No task reroll. Entry overlap inspected 633 open PR bodies and used the current overlap helper, with partial Discussion coverage. Signed-in handoff read showed no replies; attempted public updates were blocked by automatic approval-review capacity. Fresh neutral-first/3886 PR searches and main refresh, including the user-authorized publication retry, are recorded in TASK.json. No exhaustive novelty claim.

Pins: #3886 scientific head 359fe0f; dataisfire #3734 fa04103. #3886's later head changes only an unrelated workflow. Frozen predecessors are unchanged; scientific inputs are self-contained exact snapshots. Credit Jeremy Kothe #2957, #2979 and the staged-entry/retiming chain; Dugongue #3863 and ranked-pair/MathProof predecessors. Sagar Thakrar's auditor and roger-sato's adapter are reused unchanged with Arham Tahir's frame-contract attribution. They are not new independent interpreters.

New enumeration, middle-cut reduction, rational block checks and ledger by Chris R / Clear1nsight with substantial OpenAI Codex assistance. Apache-2.0 and retained notices. No human review, formal-kernel acceptance, fresh native Clifford/Gaussian, allocation, precision/tape, all-size/compiler, full outer/supplier, analytic or BIT admission is claimed. Open next questions are in README.md/TASK.json.

Open next questions

README.md and TASK.json retain the next questions. The smallest useful follow-up is one legal nonadjacent or farther neutral first word and its complete interacting second-move invoice. Coordinated frame changes through a non-neutral intermediate are also open. Both require a literal source-bound witness, arbitrary-dirty restoration and full added-cost accounting; the present exclusions do not cover those domains.

Publication heads and hosted verification

Scientific contribution head: 001ebcdb3f86a7f9d5f5897f9cf5a84e74dd1822, one additive commit containing exactly the 22 research files. A separate concurrent commit, df8e436be781ae2abb8e9e779b586f10f1165e6f, adds the inherited P112 workflow context repair in .github/workflows/p112-common-slice.yml; it preserves every research file and frozen input. The current PR therefore contains two commits and 23 changed files. The first CI run was superseded after the new commit; replacement registered replay is tracked at the current head. Its outcome is separate from the recorded local scientific checks.