Research: sharp weight-five common-frame capacity and 24-ADD witness

[ToikY]

Change and mathematical scope

Structural research result; no new κ or physical supplier. At h=9, a single legal common separator supports at most 36 signed rank-one interactions between weight-five endpoint families containing a degenerate pair on each side. An explicit 6×6 block attains this bound with twelve orthonormal residual bases. Its complete arbitrary-dirty-helper scalar word takes 24 signed ADDs, saving twelve against 36 direct entries.

The changed hypothesis is simultaneous sharing at one station, extending independently chosen pairwise completions. Two separately implemented exhaustive censuses agree on every legal frame maximum. The normalized integer kernel is used; physical phases and the inherited side-matrix factor 1/2 are not compiled. The conditional incident bill is twelve rank-three and twelve rank-four transfers, mass84, versus direct mass252. This is not a complete supplier invoice. Caller/source access, adapters, helper lifecycle, global layout/copies, recursive hosting, precision/tape and analytic transfer remain unimplemented.

Task and overlap

Fresh OS draw 48, structural track; a new randomness call happened to repeat the earlier numerical seed. Scope refined before experimentation: weight5/h9/common-U4-W5/multiway-signed-rank-one/degenerate-both-sides. Base: 1b59b62. Local claim/result records three candidates, finite domain and stopping rule. No pinned sprint issue exists, so the permitted local fallback was used.

All U4 containing a canonical degenerate weight-five pair, intersection1 or3: 5334 quotient-plane lifts, 2048 nondegenerate frames. Dimension-five separators follow by transposition. Signs are essential: some frames have nine eligible targets. No unrestricted decoder impossibility claim.

Predecessor heads: #1173 72bfdf6, #1139 82da1e8, incorporated #920 9138174. Their pairwise existence, triple classification and residual/dimension criterion are credited, not repeated. Only this new package is added; three predecessor documents retain original bytes/notices and no predecessor implementation is imported.

Live PR bodies/discussions, the ledger and prior negative results were checked. Immediate submission refresh reached #1228: its pending-range audit, #1226's masked E8 census and #1224's nine-term normal form concern different objects. This is bounded overlap evidence. Upstream refreshed to 49b3157; updated guidance was read, and all six pinned inputs, including selected record/review, remain identical.

Validation

macOS arm64, CPython3.9.6, standard library only. From the repository root:

python3 -I -O -B research/five-subset-common-frame-seed48b/test_package.py
python3 -B scripts/verify_selected_result.py

Expected final marker:

PASS_COMMON_FRAME_WEIGHT5_PACKAGE frames=5334 area=36 adds=24 controls=PASS no_new_kappa

Normal and optimized replays pass: all twelve residual bases, all thirteen input columns including dirt, literal inverse, twelve witness semantic controls, ten on-disk corruption controls and relocation to a spaced path. Missing evidence fails without regeneration. Both censuses share the complete-frame digest ac3520884ea295130595b20b4703217ed6838ba49dae1e4ca63412371803be7a. Selected-record guard passes; remote and staged Git trees match byte-for-byte. Validation details.

Not run: full selected cold replay, native admission, Linux, formalization or human mathematical review. Finite replay is not a formal proof of the multiplication theorem. No selected or upstream file changes.

Credit

Douglas Colkitt's parity kernel/obstruction; ArnavSwiggy's #920 geometry; @woklerx's #1139 classification; ToikY's #1173 and seed47 frame completion; icekylinx's general Clifford-frame ranks, plus retained format lineage. Prepared for @ToikY with substantial OpenAI Codex assistance, including two bounded workers for distinct implementations and review. AI-assisted evidence, not independent human review. Apache-2.0; exact source pins and original notices retained.

Open next questions

Next question: compile this thirteen-register word into the historical physical frame format and price every caller, boundary and phase operation. This tests whether local savings survive realization; compatible source access and helper lifecycle are blockers. The unchanged rejected global ParitySide DAG is not reopened.

[Mister-Meeseeks]

100-PR batch review at fd470c4ade3139bc8d805c77558b9d6b823a1690.

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

Reviewed scope: Exact h9 common-frame census:5334 lifts, sharp36-entry weight-five block,6×6 witness and24-ADD dirty wrapper. Conditional local edge-rank bill excludes global frame/phase/hosting obligations.

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.