Research: exact 12/13 frame281 boundary and two fewer ADDs (no new kappa)

[woklerx]

PR952's frame281 has a 13-ADD circuit. Exact positive-transfer synthesis finds a 12-ADD replacement, and rebuilding mandatory reverse cleanup reduces the complete local word 23,673 -> 23,671 ADDs. This is a finite bit construction and scoped exact boundary, not a new kappa.

The useful boundary is 12 versus 13: 12 is the exact minimum for this six-wire fixed integer transfer, while requiring entrywise domination by the original reverse matrix forces 13. The 12-ADD witness fails that local guard yet lowers the complete reverse bound 833,084 -> 832,712; F stays 41,287 and local/nine-stage charges remain 92/174 bits under 104/192.

Only research/r439-frame281-seed15/ is added. Base: bbc600db2fc15007b7c914f4f2b2ed55fa909c87; OS assignment seed15. Source hashes, literal witness, independent row/column algorithms, exact certificates, proof, scope and attribution are included. All 661 dirty-input columns, H1-H5, frame paths, exported MOVE/COPY/ERASE lifecycle and paid rank mass5,129 are checked. No selected pointer or upstream source changes.

Reproduce from repository root:

python -I -B research/r439-frame281-seed15/verify.py

Expected: PASS_R439_FRAME281 gates=13->12 local_ADDs=23673->23671 columns=661 rank_mass=5129 controls=7. This reruns discovery, independent minimum12/minimum13 proofs, nine independent controls, seven circuit/whole-word controls and canonical certificate comparison. It passed on CPython3.14/Windows with a writable process-local temporary directory.

Limitations: make verify could not start because make is unavailable. Native C++ 5/9/11-stage replay could not start because compatible GCC/Clang and Boost were unavailable; the optional harness is supplied, with no native certificate/pass claimed. Exported-record interpretation is not native execution. Hosted supplier adoption/invoices, outer assembly and inherited all-size/compiler/physical/analytic obligations remain open.

Overlap refreshed before submission: Gareth Davidson's concurrent #980, head ba1cf68bef0c97dfb120add04304e2de0db6f29c, still has the same 13-ADD frame281 block. Its broader full-prefix admission result is credited; no priority for the general admission idea or combined #980 saving is claimed. The initial selected-word matrix was recognized as conjugate to Ross Richardson's #925 result and credited, prompting the documented pivot to PR952's different transfer.

Prepared for @woklerx with substantial OpenAI Codex assistance, including scoped independent implementations. Credit retained for Gareth Davidson (#904/#952/#980), Ross Richardson (#936/#925), the #754/#691/#857/#906 lineage, and eumemic/DreamingOfClouds/native-checker contributors in NOTICE.md. Apache-2.0; no independent human review or full theorem verification claimed.