Handoff publication review — 2026-10-05

STATUS: RIEMANN HYPOTHESIS OPEN.

This is an edited public review record, not a copy of the private handoff or a publication of its research code. Research-record dates are October 1–2; the import and review date is October 5.

Adoption decision

ACCEPTED — CONDITIONAL TRANSFER ONLY. Eventual ES and strong physical L² capture of the nonzero theta kernel, on the same cofinal sequence, imply locally uniform convergence of the real-scaled ground transforms. The actual ES and capture hypotheses remain open. CMP, RH and full even-ground capture are not established.

The primary inputs checked were CCM's Zeta Spectral Triples, arXiv v1, Definition 5.3, Lemma 5.4, Proposition 5.9, Theorem 5.10(iii), and Lemmas 7.2–7.3; and Clunie–Kuijlaars (1994), Corollary 1.3, p.110, with its proof on pp.113–114. The latter original was unavailable during the supplied work but was obtained for this review. CCM · Clunie–Kuijlaars original · DOI.

The convention checks retain the full finite Weil space, zero extension, real normalization, boundary-functional nonvanishing under CCM's actual matrix hypotheses, and the scalar convention \(\widehat k=\Xi/4\). The phase factor in a regularized determinant is not treated as a real LP function. The raw proxy is not assumed exactly even.

Adversarial checks and limits

• Strong L² alone is insufficient; the new branch uses real-zero structure from ES.
• Exponential type and real type are checked before LP membership is used. Arbitrary real-zero entire functions are not substituted.
• The original CK theorem concerns polynomial zeros, not merely critical points. LP approximation on expanding disks supplies the required polynomial sequence.
• Convergence in measure is applied on an interval with a nonzero limit. Weak convergence or a zero limit would not suffice.
• Value normalization is performed only after convergence and nonvanishing at the anchor are established.
• The ordinary projection condition does not construct a sequence satisfying actual ES or capture.
• An energy/gap upper bound is not identified with a necessary capture criterion.
• The earlier ES-independent CMP-R remains valid. No prior historical update is rewritten to assert knowledge of this branch.

This was a fresh source/hypothesis check and a separate reverse-order adversarial pass by the same AI reviewer. It is not independent human peer review or formal verification. Existing general theorems were imported, not re-proved in full.

Import and numerical scope

The private intake contains 11 research units and 115 original files, with 112 distinct hashes and three internal duplicates. Eight original archive bundles were preserved privately. The transfer idea is a conditional application of existing mathematics, not a claim of a new literature theorem.

Existing seed and Fourier-projection bounds already imply the proxy L² estimate; its odd-component bound is an explicit corollary. These are not counted as newly solved actual ground estimates. Four supplied finite cases received read-only decimal consistency checks of spectral sums, parity margins, gaps and distance ratios. The eigenproblems were not rerun, and no rigorous true-prolate error enclosure or cofinal estimate is claimed.

The earlier 12-of-19 import count retains its original scope. Newly discharged actual moving-Weil asymptotic obligations: 0.

Preservation and publication scope

The new bilingual update, current-state overview, roadmap, timeline, entry links and a new dated state file are the public changes. The original October 1 update, older timeline entries, research evidence, source manifest and historical state files are retained. The private bundle, raw numerical output, conversation material, third-party papers and machine-specific information are not included in the new publication.

The public summary is available in Japanese and English. The dated state record separates an accepted conditional implication from its unproved actual hypotheses.

Build, link, language-pair, formula, mobile-display and publication-safety checks are recorded in the private reconciliation report and the GitHub Pages workflow. Passing those checks does not verify RH or the missing spectral estimates.

CMP: OPEN. ES: OPEN. EVEN FULL-GROUND CAPTURE: NOT ESTABLISHED.

STATUS: RIEMANN HYPOTHESIS OPEN.