Conditional T740 kappa refinement: +9.04e-25 over PR3148

research/coupled-cap740-grid35/CLAIM.json

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+{
+  "baseline_head": "f2927a4b8afcf0701a6b945e14f30de1d94f5176",
+  "baseline_pr": 3148,
+  "complex_lower": "8648887473392985059434518284089/5000000000000000000000000000000000",
+  "endpoint_digits": 35,
+  "fresh_native_replay": false,
+  "gain": "903656817800000000000099999999999000000000000099999999999/1000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+  "kappa": "1729777494678597011886903656817799999999999999999999998999999999999999999999999/1000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+  "physical": 663549,
+  "previous": "17297774946785970118859999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "private_zero_buffers": 91,
+  "profile": {
+    "1": 16376940,
+    "2": 4821840,
+    "3": 1567431,
+    "4": 679320,
+    "5": 147075,
+    "8": 53280,
+    "48": 282569
+  },
+  "scope": "Conditional fixed-supplier precision refinement; inherited physical/compiler/all-size assumptions remain",
+  "selected_frontier_changed": false,
+  "source_base": "6f100d4bb5083f8c35d96fd95a539811c62f245c",
+  "status": "CONDITIONAL_FIXED_SUPPLIER_PRECISION_REFINEMENT"
+}

research/coupled-cap740-grid35/NOTICE

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+Copyright 2026 dataisfire. New work under Apache License, Version 2.0.
+Prepared with substantial OpenAI Codex assistance.
+
+No predecessor source file is changed. Source-authenticated code is executed
+from the existing repository packages, retaining their notices and licenses.
+
+Retain research/coupled-carrier-cap740/NOTICE and its vendor/PR3133-NOTICE,
+vendor/PR3133-CREDITS.md and all predecessor notices; Jeremy Diviney owns the
+T740 exchange/integration and dcharb78 owns the coupled helper folds.
+Retain research/rank7-joint-endframes/CREDITS.md and its native/geometry lineage.
+The independent moment auditor is credited to its original package authors.
+The source comments of research/gmx-t74-borrow43-handoff and the retained
+adaptive-kernel-demotion/vendor/engines/outer.py preserve the outer, arithmetic,
+prime-padding, assembly, compiler, native and BIT contributions.
+This package does not claim authorship or independent reimplementation of them.

research/coupled-cap740-grid35/PROOF.md

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+# Conditional refinement and reuse boundary
+
+Let D be the literal PR3148 supplier/allocation and its complete admitted bill.
+Its paid histogram is
+
+```
+{1:16376940,2:4821840,3:1567431,4:679320,5:147075,8:53280,48:282569}.
+```
+
+Its rank mass is 65088*740; m=73 and W=896*740. For a trial saving b, the
+unchanged finite recurrence moment is
+
+    M(b) = sum_r n_r*r*(73/r)^b / (73*W).
+
+All coefficients are positive and every r<73, so M is strictly increasing.
+Both source-pinned interval engines give M(C)<1<M(C+10^-35), for
+
+    C = 0.0017297774946785970118869036568178.
+
+They additionally certify a containing 40-digit root bracket. This improves
+the endpoint certificate of the same D without asserting any new finite
+operation or changing a cost. Root arithmetic alone does not establish D.
+
+## What is reused
+
+The entire baseline package, exact native word blobs, complete admission,
+native-provider and retained-cache receipt bindings, literal allocation
+bindings and decompressed invoice are pinned. The baseline's own
+verify_release.check runs unchanged. Its native/source/receipt/status fields,
+complete T740 bill, 6660 invocation sweeps, 663549 physical families, 91 buffers
+and 1479/2048 prefix bound must pass. Its ten corruption controls still reject.
+All nine finite invoice guards are required to be the Boolean true.
+
+The finite word, frames, widths, physical roles, primitive counts and coefficient
+prefix are identical objects; the endpoint's decimal grid is a proof parameter,
+not an added scalar gate or a new physical coefficient. In particular, the
+invoice's nine fixed integer guards have no new input: no instruction, storage,
+COPY, restoration or routing cost is removed or reassigned. The changed
+recurrence inequality is checked afresh by both moment engines with the complete
+paid histogram. The unchanged assembly's _outer_witness_raw is extracted from
+the authenticated source without edits and run at C with its 2048-bit reserve,
+retained BIT endpoint and a 12-stage carried-constant bootstrap; all 47 strict
+constraints and four original rejection controls pass. Its output is a legacy
+balanced transfer point, not the final modern kappa claimed here.
+
+This reuses the *premise* that the exact source-bound native/physical evidence
+admits D at the baseline's stated conditional scope. It does not turn stored
+receipts into an independent proof of all-size, compiler, realization,
+precision/tape or analytic premises. No new cold supplier/native admission is
+claimed. If those inherited premises fail, this refinement inherits that failure.
+
+## Fresh modern outer argument
+
+Reconstruct the admitted PR3148 outer checker exactly: authenticate its original
+source hash, apply its one recorded replica-width patch, and require the exact
+admitted script hash. No predicate is deleted or weakened. Set endpoint_digits
+to 35 and regenerate all free gaps by its existing formulas:
+
+    r0 = 10^-115, delta = (1025/1024)*r0,
+    epsilon = 1-delta, beta = 1-3*delta,
+    b = C-r0, q = b-r0,
+    FLOOR = 10^81, BACKOFF = 10^-57.
+
+The checker derives its endpoint by truncating epsilon*q, rather than accepting
+the claim as an input. Its fixed-grid identity proves
+
+    K = C - 10^-81 - 10^-57.
+
+The SPEC expected.kappa field is the checker's *comparison* point. Here it is
+PR3148's previous modern K, which is stronger than the historical online
+comparison used by that supplier. The candidate K itself is derived and compared
+after execution. Using K as that comparison would require K>K and correctly fail.
+
+All 63 strict inequalities and all 17 original negative controls are regenerated.
+The unchanged independent balance checker independently derives K from the same
+exact endpoint/slacks. The strict moment condition, explicit prime/Strassen/
+gauge-free/union hypotheses and retained BIT endpoint are the same as before;
+their inherited mathematical premises are not newly proved by these computations.
+
+Finally, exact rational subtraction gives
+
+    K - K_PR3148 =
+    903656817800000000000099999999999000000000000099999999999 /
+    1000000000000000000000000000000000000000000000000000000000000000000000000000000000
+    > 0.
+
+The public CLAIM must match the freshly computed endpoint/gain and explicitly
+state that native replay and selected-frontier changes are false. RESULT.json
+must equal the whole freshly regenerated scoped result. This proves a tiny
+conditional refinement of D, not an improved word, a new global-best theorem,
+or a repair of the stronger disputed donation overlays.

research/coupled-cap740-grid35/README.md

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+# PR3148 fixed-supplier endpoint refinement
+
+Conditional kappa is
+
+```
+0.0017297774946785970118869036568178 - 10^-57 - 10^-81
+```
+
+This exceeds PR3148's published `0.001729777494678597011886 - 10^-46 -
+10^-70` by approximately **9.036568178e-25**. It is a tiny precision
+refinement of the same construction. The paid profile, literal words,
+allocation, 663,549 physical families and 91 private zero buffers are unchanged.
+The selected result is unchanged.
+
+## Evidence and limits
+
+Both retained rational moment engines accept the 35-digit endpoint and reject
+its successor; adding an unpaid rank-one or rank-48 child rejects. The unchanged
+carried-constant bootstrap runs all 12 stages and 47 strict constraints. The
+exact PR3148 modern outer checker runs all 63 strict rows and 17 rejecting
+controls, and its unchanged independent balance checker agrees on the new
+point. The full scoped result is regenerated and compared with RESULT.json.
+
+Native, owner, physical invoice and finite guard evidence is **source-bound
+reuse of PR3148**, not a fresh cold/native rebuild. Its complete stored-release
+binding checker runs, including its ten receipt/invoice corruption controls.
+All nine fixed finite guard receipts, the complete profile and the actual
+1479-bit prefix within the charged 2048 bits are retained. PROOF.md explains
+the reuse boundary. This does not supply new independent scientific admission
+of the supplier, compiler, physical hosting, precision/tape, mutable source,
+all-size realization, analytic transfer or BIT H1-H5 hypotheses. No human or
+proof-kernel review is claimed. Green arithmetic is not a multiplication theorem.
+
+Source base is `6f100d4bb5083f8c35d96fd95a539811c62f245c`, priority revision 6.
+Baseline is PR3148 head `f2927a4b8afcf0701a6b945e14f30de1d94f5176`.
+SOURCES.json binds all predecessor package bytes and every imported scientific
+source. Existing nominal higher claims #3184/#3190/#3198/#3200/#3251 are outside
+this comparison: their literal donation operators have published objections
+(#3187/#3296). This package does not claim to exceed those unadmitted numerical
+headlines or resolve their contracts. #3338/#3354 improve a different selected
+word at a lower kappa. PR3143 is an earlier T74 precision precedent; this
+package applies the refinement to the cap-attaining T740 allocation.
+
+## Reproduce
+
+From a repository checkout with the declared inputs:
+
+```sh
+python3 -B research/coupled-cap740-grid35/verify.py
+python3.12 -B scripts/research_package.py --package research/coupled-cap740-grid35
+```
+
+The package is standard-library only. Assertions must remain enabled for the
+retained outer checkers; optimized Python is explicitly refused. The direct
+verifier authenticates source bytes before compiling them and gives each child
+interpreter a fresh bytecode namespace. Optional `--output NEW.json` writes a
+fresh result; an existing output is refused. Temporary products stay outside
+the source package. The finite registered command does not rerun native chains.
+
+## Open next questions
+
+A material gain requires a changed paid word or physical contract outside the
+attained fixed-word packing cap. First supply an exact interaction and full
+producer/consumer bill, then test causality before native work. No cheaper legal
+changed supplier survived this session's bounded experiments. TASK.json records
+the structured question and limits; these private failed searches are not new
+public impossibility claims.
+
+## Credit
+
+Jeremy Diviney/PR3148 supplies the allocation and full release; dcharb78/PR3133
+supplies the coupled helper folds. Gonzalo Mier/PR3143 supplies the T74 precision
+precedent; Nick Petalas/PR3135 and dataisfire/PR3115 supply earlier T740
+precision precedents. Marius-Paul Dumitrean, Jeremy Kothe, Mason Hale, Nick
+Petalas, Arham Tahir, Sagar Thakrar and the retained native/geometry/owner
+lineage retain their contributions. The moment engines, Vlado Vojdanovski's
+outer construction, Chafik Boukhalfa's fine-prime padding, gauge-free and union
+schedule work, Tim Trudgian's cited prime result, eumemic's 47-row assembly,
+the PR589 BIT supplier and all inherited notices remain credited. See NOTICE
+and predecessor notices for the full retained lineage.
+
+Prepared for dataisfire with substantial OpenAI Codex assistance. New work is
+Apache-2.0. This contribution claims the new exact endpoint and scoped
+source-bound replay, not invention of the retained construction or engines.