Scoped negative result: no extra singleton 4-to-6 B-frame in selected k8 word

[1337isnot1337]

Result

This package proves a scoped obstruction for one precise change to the selected PR1094 complex supplier: no single unchanged B-gate output frame on its selected k8 word can be enlarged from dimension 4 to dimension 6 while preserving the later frame chains.

There are 147 unchanged 4D B-gate frames. Each has 155 possible 6D superspaces in F_2^9, for 22,785 candidate gate/frame pairs. The exact intersection of all later paid frames on both affected register chains, early cleanups, and terminal frames has dimension 4 at 122 gates and 5 at 25 gates. Every legal enlargement would have to fit in this common suffix cap, so no 6D candidate exists. The certificate records all 147 caps and the verifier includes Gaussian-count, incompatible-frame, and source-pin controls.

Reproduce

python3 -I -B research/complex-k8-singleton-frame-cap/verify.py \
  --out /tmp/complex-k8-singleton-frame-cap.json

Expected:

PASS_NO_ADDITIONAL_4_TO_6_SINGLETON_B_FRAME gates=147 candidate_space=22785 max_cap_dimension=5 chronologically_feasible=0

Base and scope

Base commit: bce54fb3f895cbe5cd4c0eb477c3afeed100190f. The selected result remains κ = 0.001672660197076918 with the complex side binding. SOURCES.json pins the selected record and source manifest, maintainer review, selected assembly and local-word replay archive, and PR1094 T16 profile plan. The selected-source head is 0fc329d0bec93ca7cd288eaea1295172e8789810.

The census changes no scalar operation, source access, copy, helper, restoration, width, owner, or call. A legal singleton frame change could only alter the local paid histogram; none is legal, so the selected complex profile and moment remain unchanged in this scope. Simultaneous frame changes, other dimension pairs, other local words, and new circuits are open. This is not a global frame-optimality result or a new κ.

The package reuses the reviewed selected replay archive and does not rerun the full selected cold replay. The inherited all-size/compiler, realization, hosting, precision/tape, analytic-transfer, and bit-interface assumptions remain; no full multiplication theorem is claimed.

Related work and credit

This uses the selected k8 word from the #1050–#1087 lineage and evaluates it under Rohan Arun's #1094 selected packing. Cinna Davis's #1090 frame/tail construction is distinct and not composed. The recent k8 gauge work in PR1263/1259 changes scalar gauges, not frame labels. A final overlap refresh covered 836 open PRs and 81 discussions and found no exact-term match; this is not a novelty certificate.

Prepared by Cinna Davis (1337isnot1337) with substantial OpenAI Codex assistance. New content is under Apache-2.0.

Coordination claim and status: #1335

[Mister-Meeseeks]

100-PR batch review at 381d4a48b3cab8c204d437627b4e76cfc0c17164.

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

Reviewed scope: Complete 147-gate suffix-cap census excludes every one-gate 4D-to-6D extension on the selected k8 word: all necessary caps have dimension at most five. Scope excludes simultaneous frame/interface changes.

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.