Certify neutral fixed-frame two-edit obstruction at displacement two

[Clear1nsight]

Close the specific neutral fixed-frame displacement-two gap released by #3957 on both immutable PR3734 staged544 providers. An existing ADD crosses exactly two scalar neighbours, retaining its source frame and zero paid delta; then any existing ADD may move to any legal scalar-corridor cut with any common binary frame. Every covered combined raw moment is non-improving for every real 0<a<1.

The new reduction scans all ADDs belonging to the reordered three-instruction block and both interior insertion cuts for outside ADDs. All other prices map to the regenerated pinned single-move premise. It does not iterate a baseline theorem on an altered word. Scalar order may change under the declared commutation/conjugation rule; native maps/cuts, entrances, exits and other frames stay fixed. No global two-edit barrier, new supplier, kappa or selected-frontier change is claimed.

Evidence

Each provider has 8,188 scalar-legal oriented first records; 154 violate frame legality, leaving 8,034 neutral fixed-frame words. Those expose 9,109,630 block-ADD prices and 4,616,377 outside-ADD interior-cut prices: 13,726,007 per provider, 27,452,014 total. All 19 signed histogram types have exact all-exponent certificates. Counts are reduced price cases, not distinct circuits.

All 16,068 admitted first blocks pass exact rational arbitrary-dirty matrices. Both baselines and 18 first plus 18 final words pass the retained complete 723-input free-operator interpreter, both orientations, reverse pullback and cleanup. Edited whole-word replays are explicitly sampled; universal dirty coverage comes from local composition algebra.

Independent controls enumerate every first admission and all 308 rejections by direct monotone register itineraries. Across 40 phase/direction/operation-pattern cases, complete incremental traces and pricing geometry match fresh reconstruction; 13,404 interior-gap prices match unoptimized full reach, and 99,150 baseline-counterpart prices match exact masks and histograms. A production mutation omitting the second interior cut changes the receipt. Source/scalar/frame/cleanup/barrier rejection controls, 24 SCALE matrices and the credited Jeremy Kothe #2957 recovery all pass, including under -O.

An early trusted-target implementation overcounted across a native B segment barrier (first B978→976, outside ADD989 at cut977). The independent full-reach control caught it. Segment clipping was corrected and both complete generations restarted from zero; interrupted attempts are excluded from evidence. VALIDATION.json preserves the failure history and precise scope.

Cost and verification

The ledger retains 3,519 baseline children, rank mass 5,134, 408 helper roles, 91 dirty buffers, all primitive/native counts, 72 native B warps and 36 initial corrections. Every first invoice equals the baseline. Second relaxed profiles have 3,519–3,521 children with unchanged rank mass. The finite all-edit numerator/denominator bound is 11 bits, not a uniform precision tariff. Fresh native phase, physical hosting/owner chronology, uniform precision/stock/tape, all-size compiler, complete outer/supplier, analytic and BIT obligations remain inherited or unknown, never zero.

python3 -B scripts/research_package.py --package research/staged544-neutral-fixed-d2
python3 -B scripts/check_research_commit.py --package research/staged544-neutral-fixed-d2 --check-source-history

Python 3.12.3 standard library: separate complete provider generations passed in 311.28s and 308.28s while concurrent. Final normal and optimized controls passed in 76.36s and 79.87s. The exact public committed-byte and full-history source gate passes for all 29 package files. Immutable snapshots are authenticated by byte count, SHA256 and Git blob; external source heads are attribution pins, not claimed ancestors.

The uninterrupted official registered replay passes at exact public head cf80e9c38b35e13bb3226a423f0246d39956ae42: both complete provider commands, optimized controls and the final PASS_REGISTERED_RESEARCH_PACKAGE marker; exit 0, 472.82s total. This is distinct from the pre-publication science snapshot recorded inside VALIDATION.json.

The official committed export passes integrity checking; its Git-free optimized controls pass in 65.26s. All export/package bytes remain unchanged. The export is a deterministic uncompressed tar (419,840 bytes), SHA256 64b67338b99e5cd2de14faee01cdcb025717666a9d7b851c8e6d2e701d0a3262. Hosted CI and independent human/formal review are separate from local execution.

Scope, coordination and credit

Adds only research/staged544-neutral-fixed-d2/, 29 files. Exact GitHub-authored head: cf80e9c38b35e13bb3226a423f0246d39956ae42; sole parent canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority 6. The full local index equals GitHub tree 5863729c98cb6c3fd1d063ce8e1152966feb4b87. Entry overlap used 662 open PR bodies plus partial signed-in handoffs. A fresh complete 672-open-PR-body cache was checked at 07:23:42 UTC with the current overlap helper; canonical main remained unchanged and no new matching neutral fixed-frame displacement-two work was found within this coverage. Discussion pagination remains partial. No exhaustive novelty claim. Scoped claim.

Credit dataisfire/#3734; #3886's single-move theorem, trace, applier and signs; #3941's adjacent-cut reduction and dirty matrices; #3942's interval pricing; and #3957's explicit gap and verification/ledger scaffolding. Retain Jeremy Kothe/#2957/#2979 and the staged-entry lineage, Dugongue/#3863, Sagar Thakrar's auditor, roger-sato's adapter and Arham Tahir's frame-contract attribution. These semantic tools are credited reuse. New three-instruction reduction, census and independent controls by Chris R / Clear1nsight with substantial OpenAI Codex assistance. Apache-2.0 and retained notices apply.

The parallel stationary-frame contribution #3964 is distinct: it holds scalar order fixed and addresses the direct-intermediate compatibility question. Here the first ADD moves exactly two positions. A useful successor changes the event graph or native/caller contract and supplies one exact before/after identity, arbitrary-dirty restoration and a full paid/physical invoice. Farther radii remain outside this package, but no automatic radius expansion is proposed. README.md and TASK.json retain concrete first steps and blockers.