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

research/tensor-syndrome-portfolio/PR.md

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+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.

research/tensor-syndrome-portfolio/PROOF.md

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+# Stage-conditioned donor-flag portfolio
+
+## Sufficient construction
+
+Take two concrete, independently checked local programs with the same source/target endpoint map and the same target labels. Each returns arbitrary dirty helpers and private work to their specified final states. Here provider11 has eleven nested-frame upgrades and provider1 has one; both additionally use the new response-preserving injection relocation. Use provider1 at stages 2,4,6,8 in all eight replicas, provider11 at all other stages. A chronological composition can replace each local program by its endpoint map because complete invocations, rather than fragments, are dispatched. Thus the existing eleven-stage endpoint identity is preserved. This requires no statistical independence between dirty helpers.
+
+For each provider, retain its exact source word hash, native record hash, local forward/reverse program hashes, starting frame list, explicit rational residual isometries, and isometry hash. Every occurrence selects its provider by its orientation and call registry. The physical assignment maps each complete residual to ONE family, an idle child, and a contiguous coordinate interval of exactly its active width. Its chronological stage lies inside that child's independently re-derived window. All selected intervals are globally disjoint. Consequently the inherited whole-family hosting theorem applies occurrence by occurrence; there is no cross-family factorization assumption.
+
+The packing selection is an explicit integer witness. Checking it needs no optimizer. Reconstruct every local program call and every remaining idle child, then count the paid ranks. Local savings and packing savings are not added. Recompute the cancellation-free row-L1 bound along every emitted scalar update on the actual physical owner families; identical-family aliases affect the same bound variable. This yields the finite precision/work invoice required by the inherited assembly.
+
+## Why the inventory choice helps
+
+The smaller-entrance provider has cheaper local frame transitions but larger residual widths. Stages 2,4,6,8 alone can access rank-7 one-stage idle children; the other stages access different windows. An identical local word everywhere ignores this difference. Configuration optimization can choose a costlier local word precisely where its smaller residual inventory saves more paid idle work. This is a compiler register-allocation / configuration-LP crossover. Heterogeneous providers themselves were already implemented in the earlier R740 weave campaign, so the novelty claim is specifically stage-conditioned choice among nested donor flags on R715, composed with response-syndrome retiming, not invention of heterogeneous dispatch.
+
+## Checked finite result
+
+Both providers passed the source-bound constructor, exact dirty columns and operand spans, native C++ legality and signed/formal columns, Gram/projector geometry, target labels, full uniform physical construction and independent audit. Provider11's first research replay reused the unchanged native executables with identical source hashes; provider1 freshly compiled them. The final portable release is to compile both afresh.
+
+The mixed independent audit passes all 62,920 whole residual occurrences, 492,240 physical coordinates, 88 complete local invocations, 72,520 logical arbitrary-dirty columns, and 19 adversarial mutations including wrong provider dispatch, wrong source hash, physical aliasing and forbidden splitting. It recomputes the full emitted program and rank inventory, and its physical prefix is 767 bits, charged 768.
+
+Complete paid profile:
+1:212216, 2:93450, 3:22776, 4:27624, 5:9944, 6:7216, 7:4248, 8:792, 36:1, 56:687.
+Live=9600, physical=9609, rank mass=745536, deficit=3264, maximum child=56.
+
+Two exact moment engines, fresh invoice, six bootstrap rounds and all 47 strict inequalities give conditional kappa = 1297375468897877 / 10^18 = 0.001297375468897877. The bit supplier binds. This exceeds PR483 by about 0.05929%, but does NOT exceed PR480's different-scope cross-copy headline. The complex supplier is unchanged and bound to its completed prior receipt in the parent campaign.
+
+## Explicit boundaries and rejected shortcuts
+
+PR480 at 668c7dd0fa76d0da4289c9dea63b965e730142d0 has headline .001372550159367980, but it assigns a single residual to two physical families and explicitly retains the disputed #448/#451 cross-copy admission. No such split is used here. PR482's non-hosting composition has .001168862033074029 and does not exceed this whole-owner route.
+
+An initial cheap pricing setup mistakenly applied the old response-packet delta a second time to stored flag-DP profiles. Comparison with the source-bound DP10/PR483 profile caught it before candidate admission; corrected input files and every actual reconstruction use the true native profiles. None of the inflated screening numbers is a result.
+
+Twelve stored flag inventories were screened using the native HiGHS integer engine through its Python interface. The full inventory portfolio was reduced to two providers to keep replay and delivery small. A root-side T84 mixed-provider screen gives only about 5.9e-9 additional bit saving and is not part of this construction. Configuration optimization is discovery only; no global optimality is claimed.
+
+All inherited all-size compiler, dirty hosting, mutable-basis, target-label, compressed-window, restoration, precision and analytic contracts remain conditional. This is not a Lean proof or an unconditional multiplication theorem.

research/tensor-syndrome-portfolio/PROVENANCE.md

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+# Provenance
+
+RECENT-PRS.json records pinned public heads and unavailable archive paths. receipts/PR483-MANIFEST.json preserves the prior full package inventory; unchanged dependencies retain original notices. inputs/PROVIDER-OVERLAYS.json binds the only provider-specific substitutions to the common source. code/retime_constructor.py is the new finite response witness checker. code/emit_portfolio.py and audit_portfolio.py adapt earlier whole-owner portfolio code and carry explicit source/program/isometry registries.
+
+The current implementation reuses the completed unchanged complex source and supports its full replay. Any completed-complex reuse must match inputs/complex-reuse-pin.json exactly. Source reads of Lean theorems guide discovery only; no new Lean certificate is asserted. The displayed kappa is a conditional finite assembly result under the inherited interfaces.

research/tensor-syndrome-portfolio/README.md

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+# Response retiming and stage-conditioned donor flags
+
+Conditional kappa **0.001297375468897877**, exactly1297375468897877/10^18, +0.059291495% over PR483. The bit supplier binds. This is a whole-family construction; it does not exceed PR480's larger cross-copy claim, which has a different disputed admission premise.
+
+Two independently checked local providers are selected by stage: one nested-entrance upgrade at stages2,4,6,8, eleven upgrades at other stages. Both use one response-preserving source-injection relocation, replacing ranks1+3 by4. All62,920 helper residuals remain whole on one physical family. Cost is recounted from the actual mixed program; gains are not added.
+
+## Reproduce
+
+    python -B research/tensor-syndrome-portfolio/verify.py /absolute/new/output
+
+Requires Python3.11+, SymPy, a C++17 compiler and Boost headers. Set CXX and BOOST_INCLUDE when these are not discoverable. The output directory must not exist and must be outside this package. No network or optimizer is used by replay. Two disposable source copies in the output receive the exact sparse provider overlays; both native providers compile afresh. They share source libraries but have independent word, entrance, isometry and selection pins.
+
+By default the unchanged complex supplier is also rebuilt. The optional --complex-output PATH reuses only the exact completed complex provider receipt and its pinned implementation/output files, checks their hashes, and emits a distinct reuse status. This is not a fresh complex execution. Fresh source-bound release receipts are retained in the outer delivery directory; VALIDATION.json records research-check scope. CI success and Lean certification are not claimed.
+
+The replay reconstructs both words, checks all955 local formal columns and dirty restoration, signed native programs, Gram/projector geometry and explicit isometries, then all88 mixed invocations/72,520 logical columns,62,920 physical assignments,492,240 coordinate slots, actual prefix and invoice, two rational moment engines and all47 strict outer constraints. Read PROOF.md and RESEARCH.md for sufficient arguments, failed searches and novelty limits.
+
+MANIFEST.json binds every package file except itself. **The hidden .gitattributes file is required**; browser upload instructions in the outer delivery explicitly create it. Preserve hashed bytes. All inherited all-size supplier/compiler, dirty hosting, mutable-basis, target-label, compressed-window, restored-work, precision and analytic interfaces remain conditional. This is not an unconditional sub-n-log-n multiplication theorem.