Conditional kappa = 0.001296606691405309: response-kernel cancellation and nested-donor flags on R715

research/tensor-response-r715/PR.md

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+Conditional kappa = 0.001296606691405309: response-kernel cancellation and nested-donor flags on R715
+
+This adds `research/tensor-response-r715/`, a source-bound offline construction and replay package.
+
+**Conditional kappa = 0.001296606691405309**, exactly `1296606691405309/1000000000000000000`: **+0.08476450% over #478** (`0.001295508560071773`) and **+0.19840410% over the pinned warm #473 claim** (`0.001294039264416565`). The bit supplier binds. This compares the complete whole-owner route; it is not a claim to exceed proposals using different admission assumptions.
+
+## Concrete new mechanisms
+
+1. **Simultaneous response-kernel cancellation.** Compute each immutable-source injection's transported target response. Delete a packet only when its response sum vanishes for every source. The useful cross-helper pair reads source3 at helpers444 and246; neither injection is removable alone. Rebuild inverse cleanup. Its local paid delta replaces rank1 plus rank5 by rank6, so strict subadditivity gives a moment improvement for every relevant exponent. Ten further duplicate pairs only reduce scalar work. Altogether22 injections and22 cleanup additions disappear, with all22 single-deletion controls rejected.
+2. **Nested-donor flags.** Replace the old one-entrance-per-donor construction restriction with an explicit sufficient flag schedule. Donors receive logical shears at increasing nested frames; all dirty values remain arbitrary. Ten pivot upgrades yield110 pivots,102 physical donors,120 correction groups and total entrance rank129. Exact response relations, frame chains and residual isometries are checked. The new constructor is explicit; the old constructor's equal-entrance guard is not silently ignored.
+
+These are combined with the new retain-and-repair #473 kernel and our14 target factors from #478. Gains are priced through the complete composed program, never added. The full local/native and physical ownership checks use the actual changed word. All88 calls use one uniform provider; all62920 residual occurrences remain wholly on single physical families. No unverified heterogeneous portfolio or cross-family split contributes.
+
+## Exact pricing and validation
+
+- Bit saving lower bound: `1298290062988365072981/1000000000000000000000000`.
+- Complex saving lower bound: `1305231506267591/1000000000000000000`, the unchanged source-bound completed supplier from #471.
+- Bit dimension78,9600 live/9609 physical families; complete rank mass745536.
+- Fresh physical prefix837bits, charged896; three-level coefficient2567bits, charged2624; row coefficient19431<20161.
+- Source reconstruction,955 arbitrary-dirty binary columns, rational frames/integer operand spans, native signed/formal columns, physical target labels, mixing controls, Gram/projectors, global owner audit, fresh invoice, both exact moment implementations and all47 strict outer inequalities pass. Mutation controls cover the changed constructors and inherited physical audit.
+
+Run:
+
+```text
+python -B research/tensor-response-r715/verify.py /absolute/new/output
+```
+
+Python3.11+, SymPy, a C++17 compiler and Boost headers are required. Replay uses no network or optimizer. Default replay rebuilds both suppliers. Our completed changed-component run explicitly reuses the unchanged complex supplier only after matching87 implementation hashes and17 output hashes against its pinned completed receipt. That mode emits a distinct receipt; it is not described as a fresh complex execution. VALIDATION.json records the actual run scope. GitHub CI is separate and is not claimed passed.
+
+## Sources, credit and retained research
+
+Direct inputs: #473 (new warm kernel), #478 (retained14 target factors), #472/#470/#467 (R715 kernels, retiming, whole-owner pooling), #463 (R715 carrier and XOR word), #450 (target mixing), #455/#476 (earlier target factoring and portable audits), and #471 (unchanged complex normalization/spectators). The retained complex/hosting/compiler lineage includes #449, #456, #457, #451, #454, #417, #442, #433, #425, #386, #377 and #370; outer assembly comes through #434/#315. #469 is credited for delivery scheduling, not its separate cross-family proposal. Upstream notices and licenses are preserved.
+
+#477's categorized experiment archive helped avoid repeating exhausted representations. #475, #474 and #397 were reviewed without counting their distinct results as numerical gains; #461/#465's sharper bad-edge charge is not used. RECENT-PRS.json records the frozen source sweep through #478 and explicitly records unavailable historical receipt files at the pinned #473 head.
+
+The library search read actual proof sources: ReasBook Woodbury/Schur update structure, Mathlib matroid exchange and subspace flags, OpenAI annihilator and SL-commutator proofs, CSLib diamond/confluence, Hadamard6 and prior tensor/CNOT project lemmas. Source hashes and sufficient mathematical proofs are retained. No new Lean kernel certification or exhaustive literature-priority claim is made.
+
+The third search lane tested noncommuting transport, GL3 basis changes, chronological affine synthesis, central-response cancellation and cleanup resynthesis. It found no admissible gain. These constructions, bounded results and C++ sources are retained for future workers; they are not advertised as a third successful technique. Previous affine-controller and heterogeneous-provider notes remain explicitly uninstantiated or unverified.
+
+## Scope
+
+All inherited all-size supplier/compiler, mutable-basis/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 optimum.

research/tensor-response-r715/PROOF.md

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+# Sufficient construction and composition
+
+This proves the finite transformations and explains their composition with the inherited conditional all-size compiler/supplier and analytic interfaces. It does not remove those interfaces or prove an unconditional integer-multiplication theorem.
+
+## 1. Retained source and target factors
+
+Start with the pinned warm PR473 word. Reconstruct the14 disjoint target-interval factors retained from PR478. If donor d gains B and receiver u originally gains A during an interval, setup u+=d, replace the receiver increment by A+B, then recovery u+=d gives (u+d)+(A+B)+(d+B)=u+A over F2. Each concrete frame/operand is checked; the scalar identity alone does not license arbitrary physical routing. These factors are inherited, not new in this submission.
+
+## 2. Simultaneous response-kernel packets
+
+For each selected source injection i, propagate its destination to the final target vector to obtain response r_i. Sources are immutable. Deleting a set S changes the final target map by
+
+    sum_s (sum_{i in S, source(i)=s} r_i) x_s.
+
+All sums are over F2. Therefore a zero response sum for each source is a sufficient certificate for simultaneous deletion, even if every selected injection is individually observable. Rebuild helper cleanup as the literal inverse of the modified helper network. Sources and all arbitrary dirty helper values are then restored; the target map is unchanged, so the original dirty-target compensation remains valid.
+
+The realized cross-helper pair reads source3 at helpers444 and246. Each single deletion fails; the pair succeeds. Its paid local delta replaces rank1 and rank5 children by rank6. For p=1-a in(0,1),6^p<1+5^p, so the recurrence moment strictly decreases at fixed rank mass. Ten additional full-frame duplicate pairs remove scalar operations without an additional moment gain. The combined packet constructor removes22 injections and their22 inverse-cleanup partners; all22 single-deletion controls fail. Backward-response certificates, all955 binary dirty columns, exact rational frame ranks and clean integer operand supports are replayed.
+
+The Woodbury/Schur and sparse-annihilator source analogues suggested the small response-product certificate U V=0. The elementary proof above is sufficient here; no inverse formula over the wrong field is assumed as a physical construction.
+
+## 3. Nested-donor flags
+
+The public constructor requires every donor to serve only one entrance frame. That is a sufficient construction restriction, not a requirement of the common-frame physical compiler. We replace it explicitly.
+
+Write a register's value in current frame F as T_F h, with logical value h. A legal climb changes the physical representation from T_F h to T_G h without changing h. At a common frame, a donor correction induces the logical shear h_d+=h_p. Therefore a donor can receive corrections at several nested frames in increasing order. Pivot/donor disjointness makes their logical shears commute; frame inclusions must still be checked for the chosen chronology. No dirty register is assumed zero.
+
+For each pivot p, the exact response relation is R_p=sum_{d in donors(p)}R_d. Thus the donor corrections cancel its otherwise uncorrected target response. Full-frame inverse corrections restore the helper logical values. A helper starting at E and ending at FULL implements T_FULL*T_E^-1; the inherited bit projector interface identifies its active residual with the complement of E. Every entrance in this witness has an explicit rational orthogonal isometry; the exact projector equations and permitted coordinate-route cost are checked.
+
+The selected word upgrades ten pivots while keeping110 pivots and102 physical donors. Its correction prefix has120 grouped rows and total entrance rank129. The actual monotone chains, all response relations, all955 dirty columns and every integer-clean operand span are checked. Deleting a selected correction or reverting its frame is rejected. An independent review recomputes the relations, prefix chains and all16 residual isometries. The old equal-entrance constructor is not invoked to justify this extension.
+
+## 4. Whole-owner compilation and pricing
+
+The changed uniform provider is used in all88 complete invocations of the eleven-stage, eight-replica controller. Every one of62920 residual occurrences stays wholly on one physical family. The new width inventory is packed by an explicit integral selection; the verifier runs no optimizer. It independently checks the complete owner array, time windows, residual coordinate slices, forward/reverse local streams and global reconstruction. No gain is obtained by splitting a correlated dirty invocation across unrelated arrays.
+
+Native legality, signed/formal-column checks, physical target labels, mixing controls, Gram data, exact projectors and independent global audit are run on the changed word. The emitted program supplies a fresh integer row-L1 prefix bound, finite precision/work invoice and row coefficient. Both rational moment implementations certify the actual complete child profile. The unchanged completed complex supplier is either rebuilt by default or reused only after checking its pinned implementation and output hashes. Six bootstrap steps and all47 strict outer inequalities then give RESULT.json's kappa. Reported improvements are composed through these profiles; they are never added.
+
+The separate research notes retain the universal packet and flag proofs, concrete witnesses, source hashes, and bounded searches that did not yield improvements. No third positive technique is claimed.

research/tensor-response-r715/PROVENANCE.md

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+# Provenance and attribution
+
+The source snapshot is frozen through PR478. RECENT-PRS.json records the changed heads, comparison with the prior sweep, and files unavailable at the pinned PR473 head. No live refresh is performed during packaging. Public claims are attributed; unchanged public verification chains were not rerun.
+
+## Direct construction sources
+
+- [PR473](https://github.com/CrocSwap/integer-mult-bounds/pull/473), head `2242365e482de3c6d230de86340896e5f46ec403`: retain-and-repair R715 kernel with110 pivots, entrance rank119 and102 donors. Its word is the source-bound input to our constructors. This is a direct reused improvement, not our new technique.
+- [PR478](https://github.com/CrocSwap/integer-mult-bounds/pull/478), head `bea1d52fd330c699903f81612ee58be81697d1eb`: our14 checked target factors, portable physical audit, and previous reference kappa0.001295508560071773. The factors are reconstructed on the new473 word.
+- [PR472](https://github.com/CrocSwap/integer-mult-bounds/pull/472), [PR470](https://github.com/CrocSwap/integer-mult-bounds/pull/470), [PR467](https://github.com/CrocSwap/integer-mult-bounds/pull/467): R715 shared kernels, retiming, stable delivery scheduling, eight-replica whole-owner packing and implementation lineage.
+- [PR463](https://github.com/CrocSwap/integer-mult-bounds/pull/463): R715 carrier/frame-pair and binary-cancellation construction.
+- [PR450](https://github.com/CrocSwap/integer-mult-bounds/pull/450): mutable target mixing and its target-label interface.
+- [PR455](https://github.com/CrocSwap/integer-mult-bounds/pull/455), [PR476](https://github.com/CrocSwap/integer-mult-bounds/pull/476): earlier explicit target prefix constructions, portable audits, and pricing. No first-use claim for prefix factoring.
+- [PR471](https://github.com/CrocSwap/integer-mult-bounds/pull/471): unchanged complex monomial normalization and same-owner spectator construction, retained as a completed hash-bound supplier.
+- [PR449](https://github.com/CrocSwap/integer-mult-bounds/pull/449), [PR456](https://github.com/CrocSwap/integer-mult-bounds/pull/456), [PR457](https://github.com/CrocSwap/integer-mult-bounds/pull/457), [PR451](https://github.com/CrocSwap/integer-mult-bounds/pull/451), [PR454](https://github.com/CrocSwap/integer-mult-bounds/pull/454), [PR417](https://github.com/CrocSwap/integer-mult-bounds/pull/417): inherited response kernels, complex pooling, whole-family hosting and physical compiler lineage.
+- [PR442](https://github.com/CrocSwap/integer-mult-bounds/pull/442), [PR433](https://github.com/CrocSwap/integer-mult-bounds/pull/433), [PR425](https://github.com/CrocSwap/integer-mult-bounds/pull/425), [PR386](https://github.com/CrocSwap/integer-mult-bounds/pull/386), [PR377](https://github.com/CrocSwap/integer-mult-bounds/pull/377), [PR370](https://github.com/CrocSwap/integer-mult-bounds/pull/370): inherited geometry, compiler and audit foundations. Outer assembly is through [PR434](https://github.com/CrocSwap/integer-mult-bounds/pull/434) and [PR315](https://github.com/CrocSwap/integer-mult-bounds/pull/315).
+
+PR469 is credited for stable delivery reordering in the parent473 lineage; its cross-family hosting proposal is not imported. PR477's categorized experiment archive informed the search and distinction between restricted failures and impossibility. PR475's complementary reservoirs, PR474's receipt binding and PR397's indexed scalar bridge were reviewed without adding their claims as numerical gains. PR461/465's sharper bad-edge charge is not used.
+
+Upstream notices, licenses and authorship are preserved in vendored code. The new contribution is simultaneous response-kernel packet deletion plus a sufficient nested-donor flag extension and its concrete whole-owner composition. This is a claim about additions to this construction, not exhaustive literature priority.
+
+## Lean/source inspiration
+
+Actual declaration/proof reads and SHA256 hashes are retained in research-notes/response, research-notes/flags and research-notes/chronological. They distinguish source-only retrieval from prior checked DAG records. Relevant structures include ReasBook Sherman-Morrison-Woodbury, Mathlib Schur block factorization, Mathlib matroid exchange/closure and basis flags, OpenAI sparse annihilator reflections and elementary transvection commutators, CSLib diamond/confluence, and prior tensor/CNOT project lemmas. Elementary sufficient proofs are provided here; no external source theorem is treated as an unproved physical compiler or cost oracle. No new Lean certificate is claimed.
+
+Historical dependency notes are retained as research-notes/PREVIOUS-PROVENANCE.md; historical heads there do not replace this release's frozen input hashes.

research/tensor-response-r715/README.md

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+# Response cancellation and nested donor flags
+
+Conditional kappa **0.001296606691405309** (`1296606691405309/1000000000000000000`), +0.08476450% over PR478. The bit supplier binds. Two new sufficient constructions are combined with the pinned PR473 warm kernel and retained14 target factors. The third library-search lane found no admissible improvement and is documented honestly.
+
+Run `python -B research/tensor-response-r715/verify.py /absolute/new/output` from the repository root. Requires Python3.11+, SymPy, C++17 and Boost headers; set CXX and BOOST_INCLUDE if needed. The output directory must be new and outside this package. No optimizer or network is used.
+
+The default verifier reconstructs both suppliers. The explicit `--complex-output /path/to/completed/run` mode checks the pinned completed complex receipt,87 implementation files and17 outputs before reuse; its receipt identifies that limited execution scope. See VALIDATION.json for the actual completed run.
+
+PROOF.md gives the sufficient construction and assembly. RESULT.json contains exact rational bounds and47 strict inequalities. PR.md supplies the title/body. PROVENANCE.md and RECENT-PRS.json record direct PR influences and frozen source pins. Research notes include source hashes, independent mathematical review, unsuccessful finite screens and retained earlier ideas. MANIFEST.json binds the final package; REPLAY-MANIFEST.json identifies the inputs used by the recorded replay.
+
+The input is PR473@2242365e482de3c6d230de86340896e5f46ec403. Constructors run in order:14 target factors, simultaneous source-response packets, nested-donor flags. Final word SHA25686ec5a244728e90714d545d0ecb8557346577f9e5c4a265b1cad844398ba4f02. Every new residual occurrence is assigned wholly to one owner. The inherited complex supplier is unchanged.
+
+All-size and analytic interfaces remain conditional. No new Lean certificate, unconditional multiplication theorem, GitHub CI pass or global optimality is claimed. Source retrieval across the registered libraries is not a fresh kernel audit.