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Finite bit construction: frame272 reaches a guarded 12-ADD minimum (no new kappa) - #1002
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Mister-Meeseeks merged 1 commit intoOct 13, 2026
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The selected PR589 bit word uses 23 ADDs in phase-A frame 272. This finite construction replaces that complete block with 12 and rebuilds its literal cleanup, reducing the complete local word 24,305 -> 24,283 ADDs. Frames, helpers, nine COPY/ERASE pairs and paid rank mass 5,129 are unchanged. No new kappa.
The independently checked boundary is 11 versus 12: 11 is the exact minimum on the six fixed wires for this positive integer transfer; imposing the selected block's reverse entrywise bound forces 12. The final 12-gate witness also satisfies the tighter PR936 reverse cap. These are scoped finite circuit minima, not unrestricted XOR optimality or a proof of the multiplication theorem.
Only
research/r439-frame272-seed06/is added. Base:407d52ff15b2217b6e22bce44728b4c3907b6515; first OS assignment seed 6. Exact source pins, literal witnesses, proof, complete cost accounting and receipts are included. The selected frontier andupstream/are unchanged.Reproduce from the repository root:
Expected:
PASS_R439_FRAME272 gates=23->12 native_adds=24305->24283 columns=661 rank_mass=5129 controls=9.Validation passed: full dirty-input and H1-H5 replay; two independent minimum checks; nine mathematical controls; 11 package tests including isolated optimized Python and tampering; fresh unchanged C++ legality and 5/9/11-stage checks on both words (883/1,327/1,549 formal columns, 96 rejected bridge controls); selected-record integrity and staged whitespace checks. Native validation used MSVC 19.51 and Boost 1.88. Hosted Linux CI and a new whole hosted invoice/outer assembly are not claimed.
Credit: Ross Richardson's #925 supplies the predecessor exact-transfer method; Gareth Davidson's #904/#952 and Ross Richardson's #936 already reduce this frame to 18 gates. The comparison is explicitly local; their whole-word savings are not added here. Concurrent #986 treats frame281, and #989 composes phase-B blocks; #989's Windows compiler adapter is credited and pinned. The final PR inventory was refreshed through #1000, with no pinned sprint issue and no frame272 overlap found among the inspected results. Original and completed local scope records are in
CLAIM.jsonandHANDOFF.json.Prepared for @woklerx with substantial OpenAI Codex assistance. Apache-2.0; full predecessor attribution and inherited compiler/physical/analytic obligations are retained in the package.