Conditional kappa = 0.001297375468897877: response retiming and stage-conditioned donor flags (+0.05929% over #483)

[Dugongue]

This adds research/tensor-syndrome-portfolio/, a standalone source-bound construction and offline replay package.

Conditional kappa = 0.001297375468897877, exactly 1297375468897877/1000000000000000000: +0.059291495% over #483 (0.001296606691405309). The bit supplier binds. This is a whole-family result; it does not claim to exceed #480's 0.001372550159367980, which uses the distinct disputed cross-copy admission.

Mechanism

1. Response-preserving injection relocation. Search the cosets of the transported target-response map, retaining only immutable-source rewrites. Move source5's injection into helper452 earlier to frame480; reconstruct the literal inverse cleanup. Equal nonzero responses preserve the target on every input, including dirty helpers. The actual witness simplifies to commuting additions into one receiver. In each invocation ranks1 and3 are replaced by rank4, strictly improving the recurrence moment for every exponent in(0,1). Deletion-only and insertion-only controls both fail.
2. Stage-conditioned nested donor inventory. Choose the one-upgrade provider at stages2,4,6,8 in every replica and the eleven-upgrade provider elsewhere. Their residual-width inventories fit different idle windows differently. Each of88 complete calls names its provider, exact word/program hashes, entrance frames and explicit isometry map. Every one of62,920 residual occurrences remains whole on one family; no cross-family split or independence shortcut enters the construction.

The crossover combines coding/control response kernels with compiler register allocation. Response-preserving retiming and heterogeneous dispatch are not claimed as newly invented mathematics: earlier gate retiming and our R740 portfolio already existed. The new concrete construction is their stage-conditioned application to R715 nested donor flags, with the new source-injection witness. The price is computed from the complete emitted mixed program, never by adding gains.

Exact result and replay

Bit saving lower bound: 1299060838562434397967/10^24. Unchanged complex lower bound: 1305231506267591/10^18.

Bit dimension78,9600 live/9609 physical families; rank mass745536 and deficit3264. Paid profile: {1:212216,2:93450,3:22776,4:27624,5:9944,6:7216,7:4248,8:792,36:1,56:687}. Physical prefix767bits, charged768; three-level coefficient2354bits, charged2368; row coefficient19431<20161.

python -B research/tensor-syndrome-portfolio/verify.py /absolute/new/output

Python3.11+, SymPy, C++17 and Boost headers are required. The frozen replay needs no optimizer or network. It reconstructs and freshly compiles both changed providers; checks native columns and signed lifts, frame/operand/projector legality, dirty restoration, complete mixed dispatch,492,240 disjoint physical coordinates and19 mixed mutation controls; then recomputes the actual finite invoice, two rational moment bounds and all47 strict outer inequalities. Default mode rebuilds the complex supplier; explicit completed-complex reuse requires the exact prior receipt plus87 implementation and17 output hashes and produces a distinct receipt. A completed reuse run is not represented as a fresh complex replay. GitHub CI is separate and is not claimed passed.

Sources and credits

Direct construction inputs: #483 (response-packet cancellation and nested-donor flags), #478 (fourteen target factors), #473 (repaired R715 kernel, and new rational84 packing as a comparison/inspiration), #472/#470/#467 (kernel, retiming and whole hosting), #463 (R715 word), #450 (target mixing), #455/#476 (prior factor/portable machinery), and #471 (unchanged complex normalization and same-owner spectators). The earlier R740 portfolio is retained and credited; this submission adapts its dispatch architecture rather than claiming to invent it.

The compiler/geometry/complex lineage includes #449, #456, #457, #451, #454, #417, #442, #433, #425, #386 and #370; outer assembly follows #434/#315. Original notices and licenses remain. Work was prepared with OpenAI Codex assistance.

The frozen sweep reads new #479 (streamed chirp phases), #480 (cross-copy hosting), #481 (batched Gaussian boundary), #482 (non-hosting target factors) and updated #473/#477. #479/#481 explicitly do not change their selected kappa, and their scalar improvements are not added here. #482 uses a different storage route. #480's larger number is kept separate because of its admission scope. #477's experiment archive prevents repeating exhausted searches;17 archive paths unavailable at its pinned head are recorded and are not replay dependencies.

Research retained for future workers

The package includes sufficient response-coset and stage-composition arguments, explicit witnesses and controls, native syndrome-search source/results, failed higher-arity searches, the complex observability screen, and a larger-replica nomination. The84-replica two-provider screen gave only about5.9e-9 extra bit saving before retiming and is not part of the achieved bound. Fourteen complex scalar-cancellation pairs left the paid profile unchanged. An initial screening double-count of an old packet delta was caught against the exact baseline and corrected before admission; it is documented rather than counted as a result.

Source-level inspirations include Mathlib's kernel-fibre identity, installed binary-syndrome sources and earlier tensor response reconstruction; no new Lean kernel audit or literature-priority claim is made. All inherited all-size supplier/compiler, mutable-basis, target-label, complete dirty invocation, compressed-window, restored-work, precision and analytic contracts remain conditional. No unconditional multiplication theorem or global optimality claim follows.

[Mister-Meeseeks]

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

Contribution: Response-preserving injection relocation and stage-conditioned donors.

Review and limits: Provider-specific widths, words and isometries are assigned to complete invocations. The simpler commuting realization and unsuccessful exploratory routes are distinguished.

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: 0c9eb6f80cef2e5797e5b7af940f447c0bdf25ad. Publication: b3c9e5c269fcfb25dfb4eda4ebc419c052d4c93d.