[chafreaky]

Change and mathematical scope

Change the per-cube local channel circuit of PR168 v4's complex word (prerequisite 4a3c769e5c5430e7114c4d3e099ff34664677f17): the local sums $A[1,0]$, $A[1,1]$ and $A[2,1]$ are assembled from direction-0 edge sums, which the $G[1,2,0]$ channel already computes, instead of edges along directions 2, 2 and 1. The circuit has 29 additions per cube instead of 27, but the carrier closure admits 11,364 arcs instead of 10,704, so the virtual auxiliary stock falls from 13,372 to 13,042 roles. All modules, fused outputs and schedules of PR168 are retained; the carrier matching, gauge selection, endpoint frame descent, 2,310 compensated handoffs and 44 terminal-output deletions are regenerated for the new graph and independently certified together with the unchanged PR168 physical bit word and the paid balanced composition. Under the retained interfaces, the bound is

$$ T(n)=O\left(n(\log n)^{1-\kappa}\right),\qquad \kappa=\frac{659180578557293}{10^{18}} =0.000659180578557293. $$

This is +0.50% over PR168 v4 (6.558894e-4) and +0.50% over my #179 (6.559202e-4), which it supersedes. The refined complex profile has 10,688 physical auxiliary roles, 13,328 persistent roles, rank mass 878,328, deficit 1,320 and largest child 20; its saving is $132438677973/(2\cdot10^{14})=0.000662193389865$. The bit branch now binds: PR168 v4's physical bit word (21,548 persistent roles) gives ordinary saving approximately 0.000659615384 after the established atom wrapper, below the complex saving, so further complex-side gains need a stronger bit supplier.

The configurable circuit is icekylinx's (PR144); this PR only selects a different configuration by a coordinate search over the 3^13 options (single-entry neighbours in three rounds plus pair/triple combinations, scored by the numerical physical root). Carrier arcs come from our own legal-edge Hopcroft–Karp matching on coordinate-padded frames, extended by DaysSky's PR162 rule, and are replayed by the retained compile_closure with its acyclicity and span checks. Scalar virtual stock, compensated handoffs, terminal deletions, the full orthogonal-group cardinality and all row reserves are charged separately. The exact four-file PR175 overlay at f1081fabbfadaaaaf7292a40d428dbbb865ce920 is retained in the verification baseline.

No mathematical hypothesis or ordinary-supplier interface is strengthened. General Clifford/tensor, uniform weighted compilation, restored-row, paid-layout, precision/recovery and analytic fixed-tape contracts remain the stated assumptions. The finite certificate is not an unconditional multiplication theorem.

Prepared by Chafik Boukhalfa with substantial Anthropic Claude and OpenAI Codex assistance. The prerequisite construction is eumemic's PR168 v4, retaining its Anthropic Claude/OpenAI Codex disclosures and earlier PR144/161 lineage. Terminal-output accumulation is James Chang's PR166; balanced-layout, atom-toll and earlier supplier attribution remain in research/paired-cube-local-168/NOTICE. PR154 supplies the isolated verification technique; PR175 supplies the exact compiler overlay.

Validation

Validated exact commit 7fb2194801e3a10f54772c7f0d5505035a4fc0ad (tree 499598ae061790f068fe61f450469ad5d0c500c9).

• The new signed graph passes the exact scalar identity, carrier closure and frame audits. Complete original and terminal-modified complex words pass in both directions, including every source/target/dirty formal column and the full target-frame chronology. The modified word checks 13,328 columns and restores all 10,688 dirty roles; three corruption controls are rejected.
• The physical bit word passes all 21,548 F2 and defining-integer-decoder columns. All 24,601 used frame Gram witnesses preserve the retained prime range; word and factor controls are rejected.
• Exact supplier moments, full scalar/group/router/row formulas, all 47 strict inequalities and seven margins pass. Independent arithmetic reproduces the same bound with 30 rejected mutations; the package retains 21 assembly controls. Adjacent grid exclusions concern only the fixed certificates and parameters.
• The read-only aggregate reproduces the canonical certificate. SOURCE.json pins 1,699 files plus its own separately reported digest; every prerequisite file is retained except the exact four-file PR175 overlay.
• Full repository gate: PASS. All 14 native verification groups plus the selected package passed in isolated copies of the published tree using the PR154 technique (Linux, 274 seconds); every source file remained byte-identical.
• GitHub CI: all 45 checks passed on the exact commit above, including the Python 3.11, 3.13 and 3.14 matrices and all formal checks.

Canonical finite check:

python3 -B research/paired-cube-local-168/verify.py

[Mister-Meeseeks]

Thank you for this contribution. Closing as incorporated into the published historical construction, with attribution retained—not as a rejection.

We rechecked the current head 7fb2194801e3a10f54772c7f0d5505035a4fc0ad and all 104 changed files. Every file is preserved byte-for-byte in the PR181 source archive used by the reviewed entrance-bank checkpoint on main. The historical implementation remains reproducible there; this closure does not select its standalone exponent as the current record.

• Incorporation evidence and exact file coverage
• Published archive and source pin
• Scoped review and contributor credit

The new central ledger separates incorporated work from pending review. Mathematical claims retain the limitations in the linked review.