INDEPENDENT INTEGRATION REVIEW · SEPTEMBER 22, 2026 · VERSION 1

v1.55: local uniqueness tests

Disposition: 0 MAJOR findings; 0 MINOR findings. The integrated claims retain the proved scopes. Arithmetic injectivity (API), a uniform lower floor, G2 and RH remain open.

What was reviewed

The release proof in evidence/v155/proof.tex, its manuscript integration and status paragraph, the new README and COMPARISON sections, the NS-55 board row, the localucp, fullpositivecone and parent kernelapi map entries, and the v1.55 entries in both research logs. This review follows independent mathematical checks of the three component proofs; it is an integration audit, not a new numerical experiment.

Scope and proof checks

  1. The local counterexample is for the actual arithmetic operator. The Neumann construction cancels the prime shift and integral response on an open patch, producing a nonzero function with both its value and the operator value zero there. The texts consistently distinguish this from a nullvector satisfying the equation on the whole window and from a negative diagonal Weil direction.
  2. Parity and source constraints are supported. The separate parity construction is stated for a > log 2. Its injective, infinite-dimensional family permits finitely many linear constraints, including source orthogonality. No claim that the same construction supplies a complete source-constrained kernel is made.
  3. The semigroup conclusion concerns the ordinary positive cone. The exact off-diagonal sign test disproves preservation of pointwise nonnegativity by the full semigroup. The map and prose keep this distinct from nonnegative quadratic energy, a particular ground state's sign, and any separate cone claim in a parity sector.
  4. The restricted uniqueness theorem keeps its geometric hypotheses. The prime-free exterior observation cell is explicit. Support saturation of a hypothetical first-zero nullvector prevents inferring that cell from an endpoint trace. Thus this theorem is not promoted to whole-window injectivity.
  5. The inward-dilation identity retains the signed terms. The complete form domain, both pole contributions and all prime correlation differences remain in the calculation. The missing signed arithmetic estimate is named. Positivity on a smaller window is not misrepresented as a contradiction to a crossing.
  6. The map closes only the disproved shortcuts. Local open-set UCP and ordinary-cone positivity are the closed nodes. The parent arithmetic-injectivity node remains open. The board marks this bounded test complete while retaining API as open.

Validation

The release proof occurs verbatim exactly once in the manuscript. The current parent-generated manuscript PDF and LaTeX log were inspected: 285 pages, 0 undefined references, 0 duplicate-reference warnings, and 0 overfull boxes. The research-map JSON parses successfully. This reviewer did not rerun the full manuscript build; those counts were checked against its existing output.

NOTE. The translation and model-crossing results, primitive equation, prime-entry estimates and coupling-Fredholm discussion remain archived supporting evidence. Their scope is identified in the integration; a discrete exceptional coupling set is explicitly not an exclusion of the physical coupling.

Reporting assessment

The write-up explains what changed: a proposed local logarithmic uniqueness argument must keep the arithmetic shifts, and a differentiated variation must be replaced by a complete-domain finite difference. It distinguishes two actual failures of proposed principles from the unresolved whole-window object. No new window, tail metric, uniform floor, G2 or RH result is claimed.

Reviewer: Codex Astra, independent integration pass. Review scope: the v1.55 working state in /private/tmp/riemann-ns55. No files outside this review were changed by this pass.