Close stationary simultaneous-frame loophole on staged544

[Clear1nsight]

Every legal simultaneous common-frame replacement at two stationary ADD addresses on either pinned PR 3734 staged544 provider admits at least one legal direct single-edit intermediate. This closes the stationary part of the illegal-intermediate question left by #3942. Scalar operators, coefficients, order, native boundaries, callers and other frames remain fixed. Gate reorderings and changed native/caller interfaces remain open.

The new result is exact simultaneous frame compatibility. #3942 already supplies the legal-sequential price obstruction in its declared corridors; the price rows here corroborate that consequence and explicitly include all stationary addresses, including 48 prelude ADDs outside its movable corridors. No new supplier or κ is claimed.

Evidence

Per provider:

• 5,549 ADD addresses; 15,392,926 unordered address pairs. 8,923 coupled pairs share consecutive events on a register; 15,384,003 factor into separately verified single edits. These are address counts, not explicit circuit replays.
• 10,591 exact nested subspace assignments, 9,883 dimension cells. Every final pair is checked against all affected boundary constraints. Zero lack a direct legal intermediate.
• 19 single and 42 joint signed-profile types, all exactly non-improving for every real 0<a<1.
• 1,345 distinct frame intervals across both providers independently checked by subset-XOR quotient enumeration.

A synthetic crossed-line pair is final-legal with both intermediates illegal; the production detector finds that obstruction. The source-bound zero is therefore not assumed as a general theorem. A naive dimension relaxation admits 100 impossible cells/provider: the actual B362/B366 proposal with dimensions 4,4 needs successor dimension at least 5. The proof explains the exact subspace-feasibility condition.

All semantic operator fields and cleanup are identical for every frame-only edit, giving the arbitrary-dirty identity algebraically. The retained complete interpreter additionally verifies both baselines and four edited whole words/provider, including A/B, A/A, B/B and restore pairs: 632 live inputs plus 91 dirty buffers, both orientations and reverse cleanup. Whole-word controls are explicitly sampled; universal family coverage comes from identical operators and exhaustive exact local legality/invoices.

The ledger retains 3,519 baseline children, rank mass 5,134, 408 helper roles, 91 dirty buffers, 72 native B warps, 36 initial corrections, all primitive counts and unchanged scalar coefficient bounds. Every changed local profile is reconstructible. No new gates/helpers/buffers are added. Fresh native phases, physical hosting/owner chronology, uniform stock/precision/tape, all-size compiler, outer/supplier, analytic and BIT obligations remain inherited or unknown, never zero.

Verification and scope

Adds only research/staged544-stationary-pairs/.

python3 -B scripts/research_package.py --package research/staged544-stationary-pairs
python3 -B scripts/check_research_commit.py --package research/staged544-stationary-pairs --check-source-history

Python 3.12.3 standard-library direct verification, normal/optimized controls and the uninterrupted official registered replay pass. The official run includes both provider commands, optimized controls and final overall PASS. VALIDATION.json distinguishes scientific author checks from later exact public-commit and hosted CI checks. No independent human or formal-kernel acceptance is claimed.

Canonical main remains 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority 6. Entry overlap covered 662 open PR bodies plus partial signed-in Discussion handoffs; exact relevant heads were inspected. This was an explicitly assigned multi-agent continuation of the PR 3942 handoff, with scoped claim. No exhaustive novelty claim is made. The expansion decision is to stop the stationary census at this closure. No selected records are changed.

Credit and next questions

Credit dataisfire/#3734 for the immutable providers; #3886 for the retained trace and sign criterion; #3942 for the legal-sequential predecessor/open question; #3941/#3957 for parallel retiming domains; Jeremy Kothe's #2957/#2979 word/frame lineage; Dugongue/#3863 for the paid rank-exchange target and #3929 for the distinct native-frame interface. Sagar Thakrar's auditor and roger-sato's adapter are unchanged, with Arham Tahir's frame-contract attribution. Full original notices and predecessor credit remain in vendor/SOURCE-CREDITS.md and the source packages. New compatibility reduction/checker by Chris R / Clear1nsight with substantial OpenAI Codex assistance. Apache-2.0.

A useful successor changes the event graph or the native/caller contract: one simultaneous moved pair with no legal direct intermediate, or a favorable complete transported-native-frame invoice. Each needs exact scalar/native realization, dirty restoration and full local/physical costs before a supplier claim. README.md and TASK.json retain first steps and blockers.

Exact public scientific head: 8a8bfb8d36cf5c9f7681b9e7f5d7876a4ba0f5a0, GitHub-authored with canonical main as its sole parent. The full local index tree equals GitHub tree 8b54252e1146ef38a6c4b98779b21df30c8c53fa. The actual full-history committed-byte/source-history gate passes for all 21 package files. External pending snapshots are byte/hash authenticated, not claimed as Git ancestors. Hosted CI remains separate.