Conditional kappa = 0.001291542455423938: two-layer target factoring on R715 (+0.1461% over #470)

[Dugongue]

Conditional kappa = 0.001291542455423938: two-layer target factoring on R715 (+0.1461% over #470)

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

kappa = 645771227711969 / 500000000000000000 = 0.001291542455423938, +0.1460538996% over #470. The source sweep is frozen through #471. This comparison concerns the whole-owner route; it is not a claim to exceed larger cross-family proposals with different admission assumptions.

Changed construction

We replace target intervals in #470's retimed R715 bit word using an explicit reversible identity. At interval entrance, add donor d into receiver u. Replace the receiver's increment A by A+B, where B is the donor's interval increment. Add the donor again at exit. Over F2:

(u+d) + (A+B) + (d+B) = u+A.

Every actual operand frame, intermediate read, dirty input and restored endpoint is checked. Seventeen disjoint target pairs form the first layer. A second layer reuses earlier target registers in a new checked interval. The construction includes18 explicit correction terms and changes only phase B. Removing any of the18 setups,18 recoveries or18 corrections is rejected.

The local paid-profile change is:

{1:-10, 2:-1, 3:-3, 4:-18, 5:+15, 6:+3}

Rank mass is unchanged. Strict concavity proves the recurrence moment improves for every relevant exponent, independently of floating search scores. PROOF.md gives the inequality and sufficient composition argument.

Every helper entrance, exit, residual dimension and isometry remains unchanged. We retain #470's eight-replica whole-owner assignment and substitute the checked program into all88 calls. No residual is split across owner families. The complex supplier is our unchanged #471 monomial-normalized, same-owner-spectator construction.

Exact results and costs

• Bit saving lower bound:646606347261404031809 / 500000000000000000000000.
• Complex saving lower bound:1305231506267591 / 1000000000000000000.
• The bit supplier binds; gains are composed through actual profiles and outer assembly, never added.
• Bit ambient dimension78; live families9600; physical families9609; whole residual occurrences62920.
• Fresh physical prefix takes808bits, charged832. The three-level coefficient takes2478bits, charged2496. The row coefficient is19431, below20161.
• The final bit profile is {1:210840,2:97761,3:19800,4:29701,5:7656,6:8632,7:4320,8:792,50:1,56:612}.

Checks and reproduction

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

Python3.11+, SymPy, C++17 and Boost headers are required; replay needs no network or optimizer. The portable verifier reconstructs both factor layers, checks arbitrary dirty columns and integer operand supports, compiles the native legality/formal-column checks, replays whole-owner emission and independent audit, checks the complex construction, then recomputes finite invoices, both rational moment implementations and all47 strict outer inequalities. Adjacent-grid and invalid-parameter controls are included. See VALIDATION.json for the completed run evidence; GitHub CI is separate.

Credits and research record

Direct sources: #470 for the retimed kernel and eight-replica whole-owner construction; #467 for the preceding R715 shared-kernel, retiming and pooling integration; #463 for the carrier/frame-pair and binary-cancellation R715 word; #450 for target mixing; #455 for our earlier prefix-factor work; #471 for our reused complex normalization and spectator construction.

The retained kernel, hosting and complex lineage includes #417, #442, #449, #456, #457, #451, #454, #433, #425, #386, #377, #370, with outer assembly through #434/#315. PROVENANCE.md and RECENT-PRS.json retain source pins and notices. We do not claim these public mechanisms as our discoveries. #461/#465 were read but their sharper bad-edge charge is not used here. #464/#469's cross-family route is not imported.

The new contribution is this explicit two-layer word and checked composition. Tensor-inspired paired coordinate changes and invariant-block ideas helped structure the search. A control search found related elementary gains through historical strict-prefix factoring, so we do not claim a new fundamental identity or first use of Schur elimination.

RESEARCH.md and research-notes preserve the useful searches, the sufficient concavity/hosting proofs, and a common-affine-offset controller theorem. That theorem's physical transport requirement is still uninstantiated and contributes no claimed gain. The notes distinguish achieved results from future routes.

Scope

All inherited all-size supplier/compiler, target-label, complete-call correlated-dirty-hosting, compressed-window, restored-work, precision, row and analytic interfaces remain conditional. This is not an unconditional sub-n-log-n multiplication theorem, a new Lean certificate, or a global-optimality claim.

[Mister-Meeseeks]

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

Contribution: Two-layer reversible target-interval factoring.

Review and limits: Intermediate reads, frames, correction terms and inverse cleanup are checked on one word. The identity alone does not establish legal physical execution.

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: e850569c33ad1d5771e2f8b1c6dfe7a445396167. Publication: 459f9dbdf41ea86f17fa21a6c71df00010a62c9b.