[ai-nanachi]

This changes the complete native BIT program and admits the conditional ordinary saving 435496247/125000000000 = 0.003483969976, up 0.24491667% from the completed PR #4814 endpoint 1737729/500000000. The exact relative gain is 1063997/434432250. This is an ordinary BIT component improvement; the selected whole multiplication result is unchanged.

The package combines the previously private G20 shadow/rank4 producer with Ali Romman's nine owned capture-relation method from PR #5421, independently rederived on the actual G20 word. G20's actual generators, native source, proof, immutable inputs and retained predecessor notices are published in this PR; it is not treated as a prior public or externally accepted result.

• The local word accepts 649 arbitrary original functions and explicitly initializes/returns 11 owned arrays to zero. Nine complete rank8 helper targets are retired; all four partial rank4 helper targets remain. Exact rational FRAME induction and paired HEAD/TAIL controls cover 660 independent RAW/DIRTY entry columns.
• The literal 18-call caller acts on 11,238 independent originals plus 11 arbitrary DIRTY owned entry columns. It pays 56,997 recursive jobs, removes 162 rank1/rank7 pairs and debits 162 rank8 targets. Every current-source descriptor binds the actual complete prefix, owner, epoch, version and geometry. Owned storage receives no productive credit.
• The same physical endpoint serves both thick-call directions, and every final job is a physical involution on the same domain. The complete program therefore supplies inverse/transpose/inverse-transpose with fresh paid owned storage, without reversing destructive erasures. Native routes, all-column and whole-ROW/spectator assumptions remain explicit.
• The new 517-bit envelope, complete positive scans/parking/routes/normalizers, eleven owned banks per compiled or suspended instance, fresh compiler/prime/cover/stock bounds and three finite completed backend levels are charged. The admitted ordinary endpoint is distinct from the raw crossing (0.0034839853304,0.0034839853305).

Reproduce with Python 3.12, standard library only:

python3 -B scripts/research_package.py --package research/bit-g20-nine-owned-relations

Validation passed: registered metadata and replay; separate literal/QQ/positive-series auditors and semantic failure controls; fresh primary and separate-audit cold replays under normal Python and -O; exact committed-byte/source-history preflight; committed export integrity and Git-free cold replay. All runtime inputs are package-local. Canonical proof payloads are compared rather than gzip headers or timing. The final documentation receipt retains the exact source-validated ancestor and the unchanged mathematical source coverage.

The construction retains the inherited native/all-column, owned-erasure, mixed-target finite compiler, completed ordinary backend, precision/fixed-tape and analytic framework premises. The enormous uniform program is algorithm-defined. No unconditional or full formal multiplication theorem, external-human audit, selected-frontier change, or optimality claim is made. Open next questions and precise coverage are in TASK.json/PROOF.md.

Credit: Ali Romman (PR #5421); DreamingOfClouds/eumemic and the PR #589/PR #555 word lineage; Cinna Davis's controller/ROW/cover work; the PR #4760/PR #4814 productive-helper and ordinary lineage; rohanarun's PR #185/#199/#204 finite bootstrap; and the unchanged exact interval/recursive sources and all retained notices. Prepared for ai-nanachi with substantial OpenAI Codex assistance. Separate internal AI reviews are distinguished from external acceptance. New work is Apache-2.0.