Finite centre-phase fanout across two shared-source panels

[1337isnot1337]

Result

This package gives an exact local interface construction for two invocations of the selected #1094 centre phase when they share the same eight source-row values and have disjoint dirty target panels. The eight rank-8 centre maps are evaluated once and their outputs are scattered to both panels. All 352 target updates are retained.

The complete two-call centre-phase invoice falls from 416 to 384 scalar actions: rank-8 moves 16→8, source copies 16→8 and centre clears 32→16, with the target updates unchanged. The exact 9-stage planning profile changes from eight to four rank-8 children per call. Under the repository's favorable relaxation this gives a_cap≈0.003212972894; the unchanged bit supplier then binds at a=0.001733427039589844234749, limiting a whole-bound gain to at most 3.4536%. This is a finite local construction and a screened cap, not a new accepted κ. The selected result is unchanged.

Evidence and reproduction

The verifier pins the selected record, review, source manifest, certificate, and the 480-helper replay archive. It reconstructs all eight selected rank-8 events and their 22 target updates, then compares the fused and separate calls over all 1,601 source, target-dirt and private-centre basis coordinates plus a dense rational fixture. It verifies three negative controls for a changed source, omitted target update and missing clear.

python3.12 scripts/research_package.py --package research/centre-fanout-two-panel-seed962302

The registered replay passes with PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=completed. Exact evidence and source pins are in research/centre-fanout-two-panel-seed962302/.

Scope and remaining work

The construction assumes identical values on the eight source rows and disjoint target panels. It does not establish that eligible invocation pairs occur in the selected supplier schedule, or charge any source preparation, owner, precision, hosting or composition cost needed to realize them. The unchanged bit supplier binds in the optimistic screen, so no selected κ follows from this result.

The scope and outcome are recorded in Discussion #1516. This is distinct from PR #1704's bit-side pair-sum scatter construction and PR #1703's one-touch rank-2 retiming obstruction.

Predecessor: Rohan Arun's selected PR #1094 and retained gauge44-slots-t16 provider lineage. Prepared by Cinna Davis with substantial OpenAI Codex assistance in scoping, cost analysis, exact verifier implementation and exposition. No human or Lean proof is claimed.

[woklerx]

Independent audit of PR#1708 at 4d163c04c0980c5b0e9092fbd5864c7cfadc125d from main 0b1cccf86e2f5132ed286a26ef0a681a495740ea.

• 88x8 scatter matrix has rank8 with176 edges.
• In common charts,zero full-panel discrepancy iff all8 centre output discrepancies vanish; source equality is necessary when each common centre map is injective.

Validation:

• Selected scatter independently extracted from emitted archive.
• Gaussian elimination and 40320-term Leibniz sum agree on determinant -1/16384.
• 64 distinct tensor basis disagreements,8 column omissions and singular-map control pass.
• Original PR1708 registered replay passes:1601 basis cases,3 controls.
• Standalone registered replay on Python 3.12.7 with the unchanged main runner passes.

Limits: Injectivity is an explicit premise; frame rank8 alone is not sufficient; No selected invocation pair or arbitrary borrowed-centre restoration claimed.

Reproduce: python3.12 scripts/research_package.py --package research/centre-fanout-scatter-rank-audit. Exact sources, original task, controls and Open next questions are in the package.

Credit: Cinna Davis PR1708; selected Rohan Arun PR1094 and retained gauge44-slots-t16 provider lineage. 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 245bb4e4b4c7669636347cd781694b21c20b2039; base 0b1cccf86e2f5132ed286a26ef0a681a495740ea. Coordinated batch, round 02.

[Mister-Meeseeks]

Batch review at 4d163c04c0980c5b0e9092fbd5864c7cfadc125d.

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

Reviewed scope: Exact two-panel fanout identity shares a centre trajectory only when the eight source values agree and targets are disjoint. Local setup and restoration are charged, and the unchanged bit cap is retained; no matching global invocation pair or complete supplier is established.

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.