RIEMANN RESEARCH RECORD · PREPUBLICATION REVIEW

v1.54: integration and claim audit

NS-51–53 · 22 September 2026 UTC · review v1

Disposition: 0 MAJOR; 1 MINOR found and corrected; 0 unresolved MINOR; 2 NOTE. The integrated statements preserve their hypotheses and open inputs. G2 and RH remain open.

Scope and identity of the reviewed result

This is a bounded integration and claim audit. It builds on this reviewer’s independent NS-51 domain derivation and checks the integration of the separately reviewed NS-52 and NS-53 fragments. It does not represent an independent rederivation of every heat-flow or approximation result, an audit of the entire historical manuscript, a numerical certificate, or verification of the eventual publication state.

The release proof evidence/v154/proof.tex has SHA-256 039eed8b6867440ba77bbe8ecc2aafe01ad9d40de5b47a1e4572d8612823cbe2. Each final source fragment occurs byte-for-byte exactly once in that release proof and exactly once in the live manuscript. The entire release proof also occurs byte-for-byte exactly once in the manuscript.

Checks performed

Complete domain and regularity. The release retains the intersection with the complete physical form domain, the local nature of the affine equation, both parity constants, and the distinction from ordinary square-integrable screw-operator injectivity. The rank-one torsion countermodel concerns the general logarithmic-principal-plus-bounded-perturbation class. Neither the release nor its new public summaries claims an arithmetic nullvector or arithmetic regularity failure. API remains an open input.

Heat transport. The normalization, analytic off-real product, exterior-cluster contribution and multiplicities survive integration. The full smooth-core zero sum is not promoted to a justified termwise differentiated sum. The single-cluster support-growth example is conditional and is not a lower bound on the full arithmetic derivative. The same-test comparison obstruction explicitly requires an unmatched real deformed zero; this checkpoint does not establish that hypothesis. No general heat-route closure is filed.

Arithmetic approximation. The residualized Schur complement and corrected correlation vector survive integration. The harmonic-trace inequality is a finite unconditional bound; its numerator is not claimed to have a proved asymptotic lower bound. RBC is sufficient and unproved, not asserted equivalent to RH or known under RH. The raw Möbius-prefix penalty is not applied to the optimal distance. The established criterion requires convergence at any rate.

Public status and internal record. The changed README, COMPARISON, AGENTS, generated research map, underlying map data, NS-51–53 board rows and both new log entries preserve these scopes. The reports state what changed and what is missing; they distinguish failure of a proposed inference or conditional comparison from failure of the original Weil or approximation object. The component cross-reviews match the final statements. Their two heat typesetting corrections are present in the final fragment.

Build evidence. This reviewer inspected the completed full manuscript log directly: 278 pages, 0 undefined/duplicate-reference warning lines, 0 overfull boxes. The integrating author ran the full build. This is not a substitute fragment build and is not described as an independently repeated build by this reviewer.

MINOR M1 — corrected before publication

The rewritten comparison correctly limited the old Li assessment to direct identification of rational Li transforms with finite-window entire test transforms. The generated map initially retained a red node naming the entire “Li / Keiper coefficients” route and saying no window could certify any coefficient. That was broader than the revised text supported.

The author renamed the red node “Direct rational Li / entire window-test identification” and limited its note to that direct identification, explicitly retaining indirect inequalities and other Li approaches. The corrected map data and regenerated README/map were rechecked. Resolved.

Notes retained

NOTE 1 — the new mechanisms remain open. A compact integral representation is not injectivity; finite collision cancellation is not a support-uniform complete transport estimate; finite block-gain identities are not convergence. The reviewed release says so consistently.

NOTE 2 — review and publication limits. This review pins the mathematical assembly above and the described claim surface. Final artifact inventories, manifest verification, rebasing or merging against moving main, and publication/tag state remain the integrating author’s checks. Historical nodes outside this changed scope have not been re-audited.

No unresolved mathematical or integration finding was identified within this review’s stated scope. The remaining repository checks still apply. No uniform floor, G2, RH, or publication-readiness claim is made.