research: certify local-first two-ADD obstruction on staged544

[Clear1nsight]

Change and mathematical scope

Add only research/staged544-local-two-add/ (20 files), at scientific commit 1416f8c. This publishes fork Clear1nsight#12 without its unrelated P112 workflow repair, which is separately submitted in #3885.

On both literal PR3734 staged544 providers, certify a local-first two-ADD retiming obstruction: the first ADD changes frame in place or crosses one adjacent ADD/nonzero SCALE; the second ADD may move any distance in its allowed scalar corridor and use any legal common binary frame. Neutral and locally losing first moves are included. With fixed entrance/exit, other gates/frames, cuts and native warps, every covered combined raw rank moment is non-improving for all real 0<a<1. Intermediate and final words must obey the boundary contract.

This is an exact reduction plus a finite census and exact sign certificates, not a global two-ADD impossibility or a new kappa/frontier claim. Longer first displacements, simultaneous edits with an illegal intermediate, gate insertion/deletion, moved SCALEs, warp/phase boundaries and changed callers remain outside scope.

Task and overlap

Canonical base: 20ecf28, priority revision 6. Explicit user-assigned continuation of #3886; TASK.json records the refined scalar-to-moment scope, frozen inputs and original overlap search. Pins: #3734/dataisfire fa04103 and #3886 scientific 359fe0f. No task reroll or exhaustive novelty claim.

A fresh publication check found #3941 (scientific 001ebcd). Its neutral-first frame changes reach displacement two and its legal adjacent commuting swaps receive a separate census. This package overlaps the adjacent neutral domain, adds locally losing first words and their changed-frame interactions, and stops first displacement at one. Neither package contains all of the other's declared domain. Counts must not be added as disjoint cases; #3941 receives parallel-work credit.

Validation

Per provider: 5,756 nontrivial first records; 1,047 changed-frame words give 11,903,025 interacting second cut/dimension checks, plus 14,693 new-gap cases, totaling 11,917,718 reduced prices and 49 signed histogram types. These are reduced price cases, not distinct whole circuits. Each provider separately regenerates all 1,776,295 #3886 single-move premise cases. The single-gap lemma and exhaustive subspace orientations avoid sampled-basis claims; oversized quotients fail explicitly.

Reproduce:

python3 -B research/staged544-local-two-add/verify.py --provider base
python3 -B research/staged544-local-two-add/verify.py --provider extra
python3 -B research/staged544-local-two-add/test_checks.py
python3 -O -B research/staged544-local-two-add/test_checks.py
python3 -B scripts/research_package.py --package research/staged544-local-two-add

Recorded CPython 3.13.5/Linux x86_64 standard-library censuses: 344.93s base and 348.66s extra. Controls include the retained exact free-operator interpreter on 632 live inputs plus 91 arbitrary dirty buffers, both orientations; independent quotient/subset enumeration on all 3,118 intervals; unpruned bridge/nonbridge comparisons; 48 SCALE-conjugation matrices; source/frame/barrier/undo rejection and predicate-disable sensitivity, normal and -O. The credited #2957 2+3 -> 1+4 recovery remains a positive control. VALIDATION.json distinguishes source-bound receipts, local schema validation with Git-pin checking disabled, and incomplete preliminary exploration that is not theorem evidence.

Hosted fork replay passed on mixed head 01742f8, whose research bytes are unchanged. That fork run is separate from the exact-head upstream evidence below. Fresh native Clifford/phase, allocation, precision/stock, all-size compiler, supplier/outer, analytic and BIT admission are unrun; no human or formal-kernel acceptance is claimed.

Passing upstream CI

Upstream run 39205949093 passed at exact scientific head 1416f8c: planning, both full provider censuses, normal and optimized control suites, and committed-input preservation. The research replay job completed in 15m31s. No repair commit was needed. This confirms registered execution; independent scientific review and the remaining admission obligations are still open.

Credit

Retain #3886, dataisfire/#3734, Jeremy Kothe/#2957 and #2979, Dugongue/#3863 and staged-entry/retiming lineage; Sagar Thakrar's auditor, roger-sato's adapter and Arham Tahir's frame-contract attribution. Reused interpreters are credited predecessor tools. Chris R / Clear1nsight prepared the new reductions, census and package with substantial OpenAI Codex assistance. Apache-2.0 and retained source notices apply.

Open next questions

See README.md and TASK.json. The smallest useful extension is a literal legal first move across at least two neighbours (especially a losing first move beyond this domain), followed by its complete interacting second-move invoice. Coordinated frame changes or changed boundaries need separate contracts. Each requires before/after words, arbitrary-dirty restoration and a full paid bill before any improvement claim.

Community uptake and coordination

The scoped community handoff gives the exact source, established result, remaining uncertainty, concrete next tasks, reproduction/runtime and predecessor credit. Independent review of the interaction/new-gap reduction and simultaneous edits outside the legal-intermediate contract are available for others to take on. Reply there with a bounded scope and investigation link, and report results here.

The displacement-exactly-two losing-first extension has a separate live claim, recorded expiry 2026-10-19T06:54:18Z; check current status and coordinate before duplicating it. This update does not override that claim. Check live overlap, including #3941 and changed-contract #3945, before starting.