Shared-edge supplier, coordinated frames and entrance banks: conditional kappa = 6.61885549259598e-4

[Dugongue]

Change and mathematical scope

Combine the shared-edge complex supplier of PR181, pinned at 7fb2194801e3a10f54772c7f0d5505035a4fc0ad, with a new compensated rematch, coordinated subspace frame cuts, and completed entrance banks on its unchanged PR168-v4 physical bit word.

Under the retained interfaces, the exact bound is

$$T(n)=O\left(n(\log n)^{1-\kappa}\right),\qquad \kappa=\frac{330942774629799}{500000000000000000}=0.000661885549259598.$$

This is approximately 0.41035% above PR181's stated bound. The complex branch binds again. Every number comes from the final combined words and paid assembly; independently quoted gains are never added.

Relative to the published PR181 witness, the matching changes 2,297 donor identities and legally retimes 1,049 compensation reads. Eleven coordinated subspace cuts change 243 distinct operation frames. Exact target chronology admits 46 terminal sinks instead of 44. The final complex profile has m=66, W=13326, rank mass 878196, deficit 1320, and largest child 20; its saving is 662323931899051/10^18.

The bit construction banks 2,200 rank-20 entrance gauges using eighteen four-coordinate cores per bank, and 15,828 other physical chains using three 24-coordinate cores. Paired rank-21 recipients remain internal splices and are not charged twice. Nine physical replicas realize every stage-private allocation integrally. The normalized bit profile is W=59144/3, rank mass 1417520, deficit 1936, largest child 22; its paid ordinary saving is approximately 0.000665064157585291.

The universal partial-swap algebra derives the completed-bank endpoint for arbitrary dirty contents. General tensor/Clifford, uniform weighted compilation, common charts, routing/restoration, paid layout, prime supply, precision/recovery, uniform setup and analytic fixed-tape contracts remain the original stated assumptions. This is a conditional finite certificate, not an unconditional multiplication theorem or a new Lean-certified bound.

Validation

The final read-only offline aggregate passes and reproduces the frozen certificate. It checks:

• The immutable LF prerequisite archive, its 1,699-file source closure, and every uploaded witness/checker file.
• Complete original and terminal-modified signed complex words, both shear signs and inverses, all 13,326 modified formal columns, all 10,686 retained arbitrary dirty registers, actual frame/target chronology, and corruption controls.
• All 21,548 physical bit columns over F2 and the defining integer decoder, original frame/prime witnesses, and word/factor controls.
• Both completed-bank partitions and inverses over F2 and Z, omitted/repeated-block controls, and the nine-copy stock identity.
• Exact paid moments, strict atom/row tolls, full scalar/group/router/row charges, all 47 strict inequalities, seven margins, and 21 assembly controls. Independent arithmetic using the original PR141 assembly and both moment engines reproduces the same bound.

Adjacent-grid exclusions apply only to the fixed suppliers and parameters. Separate integrity controls reject altered checkers, altered archive parts and unlisted source files.

Canonical command, with Python 3.11+ and assertions enabled:

python -B research/coordinated-frames-and-entrance-banks/verify.py

No network, Git credentials or third-party packages are needed. The immutable archive is split into three parts below GitHub's 25 MB browser-upload limit. Extraction and execution occur in a temporary directory.

Sources and disclosure

Developed with OpenAI model assistance. Upstream author notices and Claude/OpenAI disclosures remain in NOTICE, UPSTREAM-NOTICE.md, copied sources and the immutable archive. PR181's shared-edge selection, PR168 v4, PR144's paired-cube/compiler framework, PR166 terminal accumulation, the balanced layout, atom wrapper, frame/reuse lineage and PR175 overlay retain their original credits.

PROOF.md and BANK-PROOF.md describe the sufficient construction. FRAME-DISCOVERY.md records the actual cuts; RESEARCH-REVIEW.md and RESEARCH-IDEAS.md distinguish accepted mechanisms from tested shared-total/harmonic/Parseval routes. No global optimality or exclusive-priority claim is made.