[bitplane]

Changing the frame of every gate in the selected k8 word still cannot beat its existing favorable packing ceiling, so frame reassignment alone cannot meet the revision-3 5% improvement target. This is a scoped negative result; it proposes no new kappa.

The certificate covers all 5,413 A/B/early-cleanup gate frames of the source-pinned R480 word, with scalar chronology, endpoints, centre cut and tail membership fixed. Complete subspace enumeration leaves 1,741 free gates in 135 components. Exact rational duals check all 23,004 LP columns and match the selected paid profile at the ceiling endpoint and 5% target. Combining this local lower bound with the existing coverage law and ideal idle packing retains a < 0.001690054109089 (balanced planning kappa < 1690054109089/1001690054109089). This also covers different legal frame assignments in different invocations.

research/selected-k8-frame-ceiling includes the proof, complete duals, a separate bitset/covector/integer-root implementation, unchanged source copies, explicit replay manifest, controls and open next questions. Navinor's X4 frame method is retained and credited; the contribution is the different selected word's complete certificate and separate checker. Credit also chafreaky/PR557, ntedvs/PR776, Rohan Guliani/PR815, Douglas Colkitt/PR1240, Sagar Thakrar/PR1012, Arham Tahir/PR1605, the selected construction lineage, and Aaron Wang/navinor's complementary climb-pair census in Discussion1659.

Validation:

• Full registered Python 3.12 replay passed, including all 14 control groups and native audits on 704 columns in both orientations for the baseline and a distinct all-upper-frame assignment.
• Both mathematical checkers passed under Python 3.14.4 with -I -O -B in a relocated read-only copy; package bytes remained unchanged.
• Source pins, metadata, the 24-file package scope, and clean patch application passed. Canonical receipt: a65d7a10aed29d7d112bb12aff0a1b0466b632cd38be068f7860bf15e5f3d265.
• Final overlap refresh covered 499 open PRs and 318 discussion records with complete pagination; relevant PR heads were rechecked. Main 5cff33057a2b35adb90dddd5084d748ec66201eb preserves the selected record, task catalogue, instructions, replay hook and all nine retained inputs.

Reproduce: python3.12 -I -B scripts/research_package.py --package research/selected-k8-frame-ceiling.

Mathematical commit: 11fbeaf34609147c124323c2f5e74fc450dad931. Base: a73173f77596b0a1a115b9fed82b65183e20f7ad. One revision-3 random draw, nonce 600a2fb184f55021a1cd62892ce3a7aa, complex-mechanisms / complex-rank-shape-decoder; no reroll. Claim: Discussion1659.

Scope excludes scalar rewrites, gate reordering, changed endpoints/helper inventories, shared centre work and changed coverage laws. This does not assert frame optimality at every exponent, eliminate remaining packing headroom, or supply a full selected cold replay, native/global admission or complete multiplication theorem. Local passes are not a GitHub CI result. Substantial OpenAI Codex assistance; no independent human review.

[woklerx]

Independent audit of PR#1671 at ce130d291f5ab6dd801544886a16f62d42d86118 from main 0b1cccf86e2f5132ed286a26ef0a681a495740ea.

• Complete baseline histogram corroborated without importing predecessor frame/LP/numeric code.
• Per-phase invoice exported for A,B,early cleanup and final climbs.

Validation:

• 5413 literal gate events and3494 paid children independently recounted.
• Endpoint mass5522 plus centre64 equals5586.
• Four incidence and omitted-charge controls pass.
• Full supplied PR1671 registered replay passes:135components,23004dual columns,14control groups,native704columns in both orientations.
• Standalone registered replay on Python 3.12.7 with the unchanged main runner passes.

Limits: Supplied dual checks rerun,not independently reimplemented by this audit; No new free-frame optimality theorem,cold replay or supplier.

Reproduce: python3.12 scripts/research_package.py --package research/k8-frame-bill-independent-audit. Exact sources, original task, controls and Open next questions are in the package.

Credit: Gareth Davidson PR1671; Navinor retained X4 frame method; selected local-word and pricing authors credited in predecessor. Prepared for woklerx with substantial OpenAI Codex assistance; no independent human review claimed. Apache-2.0. No new selected kappa.

Exact committed audit artifact. Commit 8efde6a766908aba22b2ecb0f7aa1ea346e8ee90; base 0b1cccf86e2f5132ed286a26ef0a681a495740ea. Coordinated batch, round 03.

[Mister-Meeseeks]

Batch review at ce130d291f5ab6dd801544886a16f62d42d86118.

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

Reviewed scope: Complete fixed-scalar-word monotone-frame LP ceiling at two test exponents, exact interval enumeration and rational duals, independent integer-root checker, full native controls. Preserves chronology/endpoints/coverage; not a universal architectural ceiling.

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.