Scoped negative result: no relocation or Steinberg rewrite with exact reframing raises PR589's bit c (no new kappa)

[ianlibanio]

Scoped negative result; no new κ. PR589's selected R439 bit word cannot be improved by one commuting relocation followed by an exact optimum over all frame assignments. The relocation moves a phase-A or phase-B summand or gate within its phase, as an in-place split, or across the scatter. The same holds for every Steinberg 3→2 rewrite of single-source gates (PR548's mechanism): there are 659, each one F2-checked, and all are neutral under exact reframing. This settles the gate-order question that open #886 leaves open after proving frame-only optimality at fixed order. Over 891,589 interacting pairs of relocations, the second enumerated on the word after the first, 685,524 are legal. 663,741 reproduce PR589's exact profile, and the rest have one of 58 distinct profiles, each certified below. None is better.

outcome (10,886 relocation classes, 1,442,430 insertion indices)	count
no legal frame assignment (least frames exceed a COPY or target hyperplane)	2,805
optimum = PR589's exact profile	7,968
optimum strictly worse (17 distinct profiles, each certified with exact rational moment bounds)	113
optimum better	0

Method

• For each gate order, reframe.py computes forward least frames and backward greatest frames. The COPY frames are pinned, so the COPY ranks stay 7×9 and the decoder constant stays 63. Free gates split into independent components, and each component is enumerated exhaustively over all closed frames between its bounds, from the catalogue or not.
• C is the literal reverse of the z-destination gates at the full frame (H4); D is unchanged.
• One representative is evaluated per slot. A slot is a run of insertion indices with identical per-register gate sequences.
• At z = c the moment is linear in the profile. Every distinct non-base profile is then certified exactly with the repository's rational moment engine, using the inherited fallback term and PR589's idle remainder.

Controls

• Positive control. On PR555's untuned word, the search finds exactly five improving relocations, including PR589's hoist and sink. The interacting-pair search from the hoist reaches exactly PR589's published profile.
• Explicit word. The control word, rebuilt with its optimal frames, passes PR589's exact F2 replay on all 661 columns. It also passes the unchanged xcheck_p.py interface audit: H1–H5 and U/J/K/C⁻¹.
• Independent implementation, no shared code. It uses frozenset frames, fraction-free integer span tests and explicit D/C. It enumerates every insertion index and groups by any shared register. It reproduces the class count and the outcome of every class with 0 mismatches. A seed-14 sample of 2,000 interacting pairs, rebuilt by the independent move builder, agrees on every pair.
• Steinberg detection control. On a word expanded by one inverse rewrite, the 3→2 search lists the cancelling triple and restores PR589's phase A gate for gate. Both implementations agree on all 659 Steinberg optima.
• Negative controls. A non-commuting swap breaks the exact F2 endpoint, and a frame lowered below its forced bound fails nesting.

Reproduce

Standard library only; no numpy or compiler.

python3 -B research/bit589-transport-reframe/verify.py /fresh/output/dir

Expected (5 min 34 s with --jobs 10 on a 12-thread Linux machine):

PASS_BIT589_TRANSPORT_REFRAME classes=10886 legal=8081 improving=0 control_rediscovered=2 independent_mismatches=0 certified=17 steinberg=659 pair_sample_agree=2000 no_new_kappa

Add --pairs for the depth-two replay (30 min 34 s with --jobs 10), which ends with ... pair_sample_agree=2000 pairs=685524 no_new_kappa.

Scope

• Covered: the stated finite class only.
• Not covered: longer reorderings, non-interacting pairs, Steinberg rewrites combined with other moves or involving multi-source gates, other op-multiset changes, D/C/COPY/decoder/hosting changes, and other words.
• Pricing: PR589's fastc identity with the idle remainder held fixed. The C++ hosting pipeline was not rerun; it needs a compiler and Boost, and no new word arises.
• κ: the selected Conditional κ = 0.001661634653669567: four paired read exchanges on PR741's frame-coalesced word #799 assembly is complex-bound (bit 0.0017334 vs complex 0.0016644), so no bit-side result changes κ.
• Assumptions: all inherited assumptions remain. This is not a Lean proof.
• Files: only research/bit589-transport-reframe/ is added. The selected record, the PR589 package and upstream/ are unchanged.

Provenance

• Base f567884aeb8851b6e794af1184119a3bfbe1e631. Merges cleanly with main at 91a2094f; the only intervening commit is an unrelated review-batch freeze.
• PR589 word sha256 e3e301e6…da52f (= PR589 EXPECTED.json).
• Moment engine sha256 81cbc864…bb39b (= selected assembly input pin).
• Compared open PRs: Scoped negative result: PR589's bit word is exactly frame-optimal (no new kappa) #886 881f72ec, Scoped negative result: R420 adjacent A swaps force both frames #711 ebd567a2.
• OS-random assignment seed 14, bit-supplier track. No pinned coordination issue existed, so the claim is local in CLAIM.json.
• Overlap refreshed against PRs through Scoped negative result: bounded butterfly search misses the PR681 factory cost #931 (2026-10-13 13:15Z). The new R439 work (Bit supplier: save 254 R439 ADDs with four-wire prefix resynthesis (no new kappa) #904, Research/r439 block522 seed17 112112 #906, Finite construction: R439 frame 519 saves 20 complete local ADDs (no new kappa) #908, Finite bit construction: R439 frame 524 saves 28 complete local ADDs (no new kappa) #914, Bit supplier: save 11,097 R439 ADDs with guarded target-basis compensation (no new kappa) #915, Finite bit construction: R439 frame520 uses 29 ADDs, four fewer complete ADDs than PR844 (no new kappa) #923, Finite bit construction: R439 frame 267 reaches a 12-ADD positive-transfer minimum (no new kappa) #925, Finite bit construction: two-sided R439 compensation saves 1,228 more ADDs beyond PR915 #926) consists of native ADD-count constructions, not paid-profile searches. Other relocation or reorder searches concern complex-side objects (Scoped negative result: certify one K-triangle relocation neighborhood #687, Scoped negative result: selected CK B frames are optimal at fixed boundaries #698, Research: save 62 CK primitives per orientation by relocating one scale (no new kappa) #750, Research: exact frame search certifies #741 and #626 providers frame-optimal (rediscovers #741; negative result) #815, Scoped negative result: SW4 pre-read insertion slides do not change the complex cost (seed 20) #910). None searches gate order or Steinberg rewrites with reframing on the bit word.

Credit

The work builds on:

• eumemic: PR543/PR555 and xcheck_p.py;
• DreamingOfClouds: PR545/PR510/PR589, wlib.py and fastc.py;
• Dugongue (PR541/PR548) and rohanarun (PR542): the transport and Steinberg mechanisms;
• SethBurkart123 (PR886): the bounds-and-components method;
• thakrarsagar (PR711) and yuj1r0 (PR661): the R420 analogues.

Prepared by Ian Libânio with substantial AI assistance (Claude Opus 5.5, Anthropic, via Claude Code). Apache-2.0.

🤖 Generated with Claude Code

[Mister-Meeseeks]

100-PR batch review at b9348c6907516e55dc07e135ad4d7a480d4f9840.

This remains open after scoped triage. Next review step: Large exhaustive reframing/reordering exclusion requires exact domain/optimality audit and a dedicated long replay, not bounded solver status.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

Batch review, attribution and evidence. Thank you for the contribution.