Research construction: shorten historical R480 quad 1 by 12 XORs (no new kappa)

[FanPUYen]

The historical #503/#510 R480 word's phase-A quad 1 has an exact 18 → 12 XOR replacement. Its literal reverse cleanup saves six more: complete local ADDs 33,958 → 33,946. This is a finite bit-circuit research construction; no new κ.

The full six-input positive integer transfer is unchanged, and the reversed nonnegative matrix decreases entrywise. Both fresh interpreters check all 720 input columns, including 480 arbitrary dirty helpers. All 720 frame paths, nine copies/erasures, and the complete paid histogram {1:1200,2:1440,4:180,6:120,8:9} remain unchanged. No temporary register or unpaid restoration is introduced.

Only research/r480-quad-seed1/ is added: frozen recipe, exact certificate, bounded nomination, proof/accounting, independent set-valued replay, optional source-pinned native replay, validation and attribution.

python3 -I -B research/r480-quad-seed1/verify.py --out /tmp/r480-quad-seed1

Expected: PASS_R480_QUAD_SEED1 quad=1 XORs=33958->33946 saved=12 columns=720 controls=20 kappa=unchanged.

Validation passed:

• Ordinary and optimized Python, independent support-set replay with 16 controls, reproduced seed-1 recipe, and a minimal offline copy in a path with spaces.
• Unchanged inherited C++ legality and five/nine/eleven-stage replay: 960/1,440/1,680 columns, all 6/18/24 omitted-bridge controls, word/interface/record controls and 672 exact frame checks.
• Native forward prefix stays 176,135; reverse decreases 3,751,204 → 3,751,140. Payload stays within 102 bits (<104).
• Source, recipe, Boolean-type and expected-evidence corruptions are rejected; selected-record check at the experimental base and staged whitespace checks pass.

One required make verify attempt in an untouched detached base passed two historical audits, then failed because system Python 3.9.6 lacks int.bit_count in inherited code. No full-suite pass is claimed. The focused native replay passed with Python 3.12.14, Apple clang 21 and Boost 1.86. Global hosting/invoice/outer assembly, Lean and remote CI were not rerun.

Experimental base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. #503: 3f27147013fdd4fa0aed825cb47bff3376c452eb; #510: 64edee18af02aab0c1696b677a0287dd0146381b. Main advanced during the work to 7ee02b7c96d85f22b38d28bd7ed49bb8c1aeb261, selecting #741/#589 at κ=0.001661202643272239. Its selected record/review were read; every consumed circuit/checker input is unchanged. The mutable selected pointer is context, not a replay dependency.

OS-random seed 1 assigned the bit-supplier track. Three candidates were considered; one attempt on R480 quad 1 found the witness and stopped. No optimality claim. No pinned sprint issue existed, so the claim is local. Final overlap refresh through #816 found no R480 quad resynthesis.

Credit DreamingOfClouds (#503/#510), eumemic (#493), and their retained predecessor notices. @mtpsl's #691 supplies related positive-integer/reverse-domination work on R420 quad 13; this checks a different historical circuit, with fresh native multistage evidence. No pending implementation is imported or combined. Prepared for Hao Yan (@FanPUYen) with substantial OpenAI Codex assistance, Apache-2.0; no independent human review claimed.

The paid recurrence is unchanged. All-size/compiler/common-label/mutable-basis/hosting/precision/tape/analytic assumptions remain inherited; finite verification does not prove the full multiplication theorem.

[Mister-Meeseeks]

100-PR batch review at 83d547e30fed98682ffc6eacbeeaafa96cfb42fb.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Historical R480 quad replacement saves twelve complete XORs with all dirty columns and frame paths retained; optional C++ replay not claimed.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

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