Bit construction: 55 same-frame rewrites on composed R439 save 110 ADDs

[ToikY]

Change and mathematical scope

Finite bit-circuit construction; no new kappa or supplier adoption. On the frozen complete PR1122 A/B/star-D word, 55 same-frame commuting Steinberg rewrites reduce 10,652 → 10,542 ADDs, including literal cleanup. Every physical MOVE path, COPY/ERASE record and actual paid rank histogram remains unchanged (rank mass 5129).

Positive prefixes improve from F=15223 / B=3910388 to F=13721 / B=3663878. Exact local/nine-stage envelopes require 91/174 bits, below strict inherited 104/192 caps. All source access, helpers, restoration, copies, bridges and recursive ranks remain charged.

The inherited syntactic H2 and K_equals_D flags remain false; all other owning H/K checks pass. Finite endpoints and precision do not establish selected hosted-supplier adoption or the complete multiplication theorem. PR1194's pending semantic-D proof is acknowledged but not adopted.

Task and overlap

OS assignment seed16, bit-supplier track. Base 1b59b62. Scope key: R439-ABC-star/commuting-z-triangles/complete-word-and-precision; three candidate tasks and local claim/result receipt are in CLAIM.json. No pinned coordination issue existed; the discussion board was read.

Pinned predecessors:

• PR1122: a2551e7, complete composed input.
• PR1127: 2e9dc9d, commuting-triangle method on the different PR589 word.

Final overlap refresh covered new PRs through #1205. Concurrent PR1188, head 6e142e7, has the smaller 10,492-ADD sibling via five-wire shortest programs. This is not an ADD-count record. Our independently checked alternative has a smaller backward bound and exact local/nine envelopes: nine-stage upper 22973795977533615901914742933524089773622692690264064 (174 bits) versus its 24941709210337926871896158204497246778939630375927808 (175 bits). Its frozen word and original notice are retained solely for independent literal endpoint/invoice comparison; its GL5 optimum is not replayed or claimed here. Sibling savings are not assumed additive. PR1181's provenance/credit receipt is also acknowledged.

Validation

BOOST_INCLUDE=/path/to/boost python3 -I -B research/r439-abc-zrewrite-seed16/native.py

Expected: PASS_R439_ABC_ZREWRITE_NATIVE: 2 words; 5/9/11 stages; 96 bridge controls; rank_mass5129; no_new_kappa.

• Independent occurrence-aware witness reconstruction imports no discovery code; all five phase maps and 661 arbitrary dirty input columns pass in both full orientations.
• Normal and optimized quick certificate replay pass; 11 negative controls reject, including noncommuting insertion, wrong duplicate occurrence, COPY/ERASE omissions, nonliteral cleanup and strict equality at precision caps.
• Fresh unchanged native legality and 5/9/11-stage checks cover 883/1327/1549 columns, exact complete scalar/bridge/copy invoices, all ordered frame paths and 96 omitted-bridge controls.
• Discovery reaches its bounded fixed point in three rounds (54 A moves, one B); regeneration is byte identical. Final census: 417 occurrences, 79 cross-section and 338 noncommuting. This is not a global optimum or impossibility result.
• All 17 retained repository dependency pins match; exact source AST binds the precision formulas. Selected PR1094 certificate guard and staged whitespace check pass.

Tested on macOS, Python3.9.6, Apple clang21, Boost1.87.0. Only this new research directory is added. Selected frontier, upstream/ and frozen predecessors are untouched. No repository-wide historical suite, selected hosted cold replay, Linux replay, hosted CI success or independent human review is claimed. See VALIDATION.md for complete receipts and unrun obligations.

Credit

Gareth Davidson (@bitplane) PR1122/1188; Aaron Wang (@navinor) PR1127/1015; Sagar Thakrar PR1062/1181; Ross Richardson PR936/923; Sricharan Vagvala PR967; Dugongue PR541/548; DreamingOfClouds PR589 on eumemic PR555/543; and the retained native-checker lineage. Original notices/licenses and exact source pins are included.

Prepared for @ToikY with substantial OpenAI Codex assistance, including two bounded workers for discovery and native verification. Apache-2.0.

[Mister-Meeseeks]

100-PR batch review at 24c45725f7b9ffca4529b46661acf343ce93cee3.

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

Reviewed scope: 55 same-frame rewrites on the complete ABC/star-D word, full native 5/9/11-stage invoice and bridge controls; gains not added to incompatible words.

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.