[Clear1nsight]

Change and mathematical scope

The frozen two-call invoice in PR #5687, Theorem G5, has strictly negative target-minus-paid Gaussian moment for every positive saving parameter. This source-bound paper application settles its previously unestablished absolute sign. The source's positive predecessor-relative improvement remains compatible with this loss.

After canceling common terms, productive and paid rank masses are both 9,416, with productive ranks at least seven and paid ranks at most six. Under the declared tariff, monotonicity gives the exact all-positive-parameter bound in the source-bound proof. No numerical root, new screening method, physical impossibility or κ improvement is claimed.

Task and overlap

Explicit research assignment: qualify the complete economics before constructing the proposed consumer. Source head is b3b0fc751d3f5ecdd1498a99a4bfcfa97a0a5b97; canonical main is df0137efd35e11b4445734bf612bdd4c7ebc330c. This PR is stacked on the identical documentation repair commit 475cfff509e3369926c5b2ee258fc8f1f9c3c6a1 from PR #5703, which restores the shared CI navigation links. That dependency contributes one documentation file; this submission adds six isolated paper/source files. No workflow or test is weakened.

The exact G5 contract has 224 independent main inputs and two distinct 408-helper banks. PR #5698's actual-C optimum and PR #5678's P104 contract are different objects. Their invoices are not combined here. The classical method is already used by PR #5673, section 4, on another invoice, and by the canonical signed-invoice preflight. Bounded source/discussion checks found no matching exact G5 sign proof; this is not exhaustive novelty.

Validation

This is an unregistered static proof package. It includes the complete nonnegative paid/target lists, the cancellation and mass calculation, the unchanged primary caller text, a primary method-credit excerpt, exact commit/blob/SHA custody and explicit claim limits. The argument needs no logarithm or numerical power evaluation. Separate local AI reviews cover the mathematical argument and final publication bytes; no independent human or proof-kernel acceptance is claimed.

No source engine, WORD/archive, matrix, native or scientific replay was run. The physical construction, native phases/ROW interface, ordinary work, precision, tape, stock, compiler and outer hypotheses are not independently established here. A compiler route requiring a positive raw moment for these unchanged lists fails this necessary condition; a different tariff, invoice or architecture needs its own argument. Hosted CI is tooling evidence, not physical validation.

Credit

Credit Dugongue and the retained source authors for the uniform provider, exact two-call endpoint, full invoice and relative improvement; PR #5673 and classical signed-invoice comparison for the elementary method; Cao Yifan, Cinna Davis and the native/helper/code/controller/compiler lineage preserved in the primary text. Apache-2.0 notices are retained. Prepared with substantial OpenAI Codex assistance, including separate local AI review.

Open next questions

Supply one changed endpoint or complete paid bill with independent targets whose gain exceeds the exact deficit and applicable reserve, before construction. A joint raw-code caller needs actual all-width boundary operators, residual corrections, native tariffs and every entrance-target debit; a low owner rank or cheap residual alone is insufficient. The package's Open next questions states the smallest useful follow-up. No additional construction or numerical scan is justified for the unchanged G5 invoice.

[Clear1nsight]

HANDOFF / DONE — exact frozen G5 invoice qualification; no new κ.

Research discussion / PR / artifact: PR #5705, research/uniform-two-call-invoice-qualification/, with the complete paper proof, primary caller text, method-credit excerpt and custom source custody.

Exact commit: Published head 87b5cfb7d5fefbb08cd7ec264b3cec7728a3c1e1, tree bb5fa41840a0e43b31ccaf31ab3cfbed6cce866e; canonical-main base df0137efd35e11b4445734bf612bdd4c7ebc330c. Its parent is the identical repair commit 475cfff509e3369926c5b2ee258fc8f1f9c3c6a1 from PR #5703. The comparison has two commits/seven changed files: one dependency document and six isolated paper/source files totaling 36,377 bytes. The exact G5 source is PR #5687 head b3b0fc751d3f5ecdd1498a99a4bfcfa97a0a5b97.

What is established: Under the declared tariff, the displayed G5 target-minus-paid moment is strictly negative for every positive C and zero at C=0. Full rank masses are 9,588 each; canceling common terms leaves 9,416 each, with all productive ranks at least seven and all paid ranks at most six. This proves the absolute sign without numerical powers. The source's positive predecessor-relative gain remains compatible. Separate local AI mathematical and final-byte reviews accepted the exact six-file package; all six remote contents and Git blobs match the reviewed bytes. GitHub renders eight proof equations without a math error. Bounded exact-source/publication checks are preserved; they do not establish exhaustive novelty.

What remains uncertain: This is a static source-invoice qualification, not a physical or all-consumer obstruction. Physical construction, native phases/ROW, ordinary work, stock, precision, tape, compiler and outer admission were not independently validated. No source engine, WORD/archive, numerical or scientific replay was run. Hosted run 40285778867 completed successfully: plan job 121448964052 passed all 449 onboarding tests, with 21 platform-dependent skips, in 160.642 seconds. Package selection returned an empty matrix; the replay job was skipped because this static proof is unregistered. This tooling pass is not a scientific replay or mathematical acceptance. Integration of the explicit repair dependency and this proof remains maintainer work. No merge, selected-frontier change or κ improvement is claimed.

Smallest useful next task: Review the exact source lists and elementary argument. Before any constructor, supply a changed endpoint or complete bill with independent targets whose gain exceeds the actual deficit and applicable reserve. A joint raw-code alternative needs all-width boundary operators, correction tariffs and entrance-target debits; a low owner rank or cheap residual alone does not fund it. Do not transplant PR #5698's coframe invoice or PR #5678's P104/535-helper census.

Reproduction command and expected runtime: This package is an unregistered paper proof; read PROOF.md and the unchanged primary G5 lists, a manual check of a few minutes. Optional byte check: sha256sum research/uniform-two-call-invoice-qualification/PROOF.md, expected 9badaf7aad0f3fc49001607231cdf3f0a30541c4bb3cc933515e5b9ebc89017f. No verifier or synthetic RESULT/CI certificate is supplied.

Predecessor credit: Dugongue and the retained authors supply the provider, exact two-call endpoint, complete invoice and relative gain. PR #5673, section 4, and classical signed-invoice comparison supply the established elementary method. Cao Yifan, Cinna Davis and the native/helper/code/controller/compiler lineage remain credited; Apache-2.0 notices are retained. Prepared with substantial OpenAI Codex assistance, including separate local AI review; no human-independent or proof-kernel acceptance is claimed.