Conditional kappa = 0.001295508560071773: fourteen target factors on PR473 (+0.1226%)

[Dugongue]

Conditional kappa = 0.001295508560071773: fourteen target factors on PR473 (+0.1226%)

This adds research/tensor-r715-next/, a source-bound offline construction and replay package.

kappa = 1295508560071773/1000000000000000000 = 0.001295508560071773, +0.1225826043% over #473. The source sweep is frozen through #475. This compares the whole-owner route, not larger cross-family claims made under different admission assumptions.

Concrete contribution

Starting from #473's reordered #472 R715 word, insert14 disjoint reversible target-interval factors. Each replaces paid children of ranks1 and4 with one of rank5. The complete word changes only phase B; helper entrances, endpoints, residual dimensions and ownership are unchanged.

The identity is (u+d)+(A+B)+(d+B)=u+A over F2. Actual intermediate reads, integer operand support and frame chronology are checked. Strict subadditivity proves the improvement for every recurrence exponent between0 and1. This is a new checked witness and composition using inherited interval/prefix factoring, not a claim of a fundamentally new identity or literature-wide priority.

Substitute the word into all88 calls of the eight-replica controller. All62,920 helper residuals stay whole on one physical family each. Combine with our unchanged #471 complex supplier, including its paid monomial normalization and same-owner spectators. Gains are computed from the combined profiles and outer assembly, never added.

Exact accounting

• Bit lower saving: 648594539814231988799/500000000000000000000000.
• Complex lower saving: 1305231506267591/1000000000000000000; the bit side binds.
• Bit dimension78; live families9600; physical families9609.
• Fresh physical prefix737bits, charged768; three-level coefficient2265bits, charged2304.
• Row coefficient19431, within20161.
• Local profile delta: {1:-14,4:-14,5:+14}.

RESULT.json supplies full exact profiles, invoices and all47 strict inequalities.

Reproduction and evidence

python -B research/tensor-r715-next/verify.py /absolute/new/output

Python3.11+, SymPy, C++17 and Boost headers are required. No network, optimizer or Lean is needed. The default rebuilds both suppliers. Explicit --complex-output /completed/previous/output checks the exact completed complex receipt,87 unchanged implementation files and every pinned complex/provider output; this emits a distinct reuse status. See VALIDATION.json for the mode actually completed, rather than inferring fresh complex execution from a reused receipt.

Changed checks include source-derived reconstruction,955 arbitrary-dirty columns, exact frames and integer spans,28 omission controls, fresh native legality/formal columns, physical target-label checks, Gram/projector identities, whole-owner emission and independent audit, fresh intermediate-growth accounting, both rational moment engines, six bootstrap levels and47 strict outer inequalities. Adjacent-grid and invalid-parameter controls are retained. GitHub CI is separate and is not claimed passed.

Credit and research record

Direct lineage: #473 reordered deliveries; #472109-pivot/rank120 kernel and hosting integration; #463 R715 carrier/XOR word; #467/#470 kernel/retiming/pooling development; #469 the delivery-reordering idea only; #450 target mixing; #455 our earlier prefix work; #471 the reused complex construction. The earlier tensor-schur-r715 release supplies the portable interval constructor and audit.

Kernel/hosting/compiler and complex ancestry additionally includes #417, #442, #449, #456, #457, #451, #454, #433, #425, #386, #377, #370, with outer assembly through #434/#315. Pinned sources and original notices are retained. #475, #474 and #397 were reviewed but contribute no claimed extra saving here. #461/#465's sharper bad-edge charge is not used.

Three tensor-inspired searches are documented in RESEARCH.md: target-basis elimination, observable-state pruning and complete-provider portfolios. The broader two-donor and observable-state screens produced no extra admitted gain. A positive heterogeneous-provider nomination remains unverified at the physical-program/invoice level and is explicitly excluded. Earlier affine-controller research is also retained without counting its uninstantiated transport condition as a result.

Scope

All inherited all-size supplier/compiler, target-label/mutable-basis, complete-call correlated-dirty hosting, compressed-window, restored-work, precision, row and analytic interfaces remain conditional. No unconditional sub-n-log-n theorem, new Lean certificate, global optimum or unsupported novelty claim is made.

[Mister-Meeseeks]

Thank you @Dugongue. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Fourteen target factors on the reordered R715 word.

Review and limits: Ranks one and four coalesce into rank five only at certified legal cuts. The unchanged complex component may be reused only with exact implementation/output bindings.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: bea1d52fd330c699903f81612ee58be81697d1eb. Publication: 2ccf3fb7887d6ba103fb3abd5a62dce992713d9f.