Conditional κ = 0.001661634653669567: four paired read exchanges on PR741's frame-coalesced word

[jeremykothe2]

Summary

Conditional κ = 0.001661634653669567. This is +4.32×10⁻⁷ over PR741 (0.001661202643272239). The complex side binds; PR589's bit supplier gives 0.0017334.

Construction, on PR699's word (sha d232183f):

1. chafreaky's PR741 frames: the 8 B-gate frame raises (dim 4→6), imported byte-identically from PR741's recipe, with its 10 frame mutation controls. This step rebuilds PR741's word e7804702.
2. X4, new here: four paired read exchanges. For each of the copy-pair pairs (448,472), (458,592), (470,604) and (482,614), both pairs' phase-B target reads are exchanged under the PR699 sw4 rule (pre-reads deleted or inserted so every register's end-of-B value is unchanged; exact Fraction check). The moved reads keep their original stored dim-6 frames instead of being refit to the minimal join, and that is where the gain comes from. Each pair on its own is exactly neutral; the two pairs of an instance together give +1.08×10⁻⁷, and the four instances are exactly additive. Profile Δ {1:−8, 2:+4}, widths unchanged (3778).

Owner map: PR741's map (the same file as PR699's), unchanged. An exact packing relaxation already proved it optimal for this window geometry, and X4 changes no widths or windows.

Construction drivers: construction/frames/ (PR741's recipe, build and 10 frame controls) and construction/jx/ (standard-library builder, explicit edit recipe, 7 pinned controls: identity, PR741-only, a single pair is neutral, dropped pre-read and wrong sign rejected by exactness, minimal-join refit is lower, and a dim-7 frame is rejected by the cap). All verifier code is byte-identical to PR699's reviewed set.

Search coverage: all 602 single-pair read subsets and all 5,880 combinations over the 40 target-sharing pair-pairs (24 legal, exactly these 4 positive); triples and larger sets were also searched. Three independent searches found the same four instances. An exact global frame optimiser confirms the word is frame-optimal at fixed gate order.

Independent review: SOUND (details in the review comment). The reviewer reproduced both steps byte-identically, found the 64 edits equal the sw4 rule, confirmed that no surviving gate changes frame, ran an exact replay (0 bad rows, dyadic, all orientations) and audit_local, checked that all 7 controls hit their pins, and rejected 8 extra mutants.

Verification

From a fresh clone of commit 80e6463, with no reused artifacts (Windows, CPython 3.11.11):

• verify_manifest.py: PASS, 132 files
• reproduce.py, reproduce_notri.py, reproduce_np.py, reproduce_p6n.py, reproduce_promo.py --k p6n-k4, reproduce_sw4.py: PR699's word rebuilt, with every layer's controls
• reproduce_jx.py: X4 word 1e1d99ba rebuilt, all 7 controls at their pinned outcomes
• audit_local.py: PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES
• verify_global.py: PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY 0.001661634653669567

construction/frames/reproduce_frames.py independently rebuilds PR741's word e7804702 (exercised by the reviewer).

Scope

Conditional on PR645's premises and PR589's bit-supplier assumptions. No unconditional theorem or Lean certification is claimed.

Credits

• chafreaky (PR741, PR685, PR660): the 8 frame raises, the owner map and the exact-flow packing.
• icekylinx (PR645): gauge44 construction, package and verifier.
• PR589 lineage (bit supplier); the PR601/604/617/622/627/635 lineage and every upstream contributor credited in PR645.

Prepared with Claude Code (Anthropic).