What was already known
The paper compares its result with the previous 5/12 unconditional proportion bound.
What changed and why it matters
Substantially raises a longstanding unconditional proportion bound from 5/12 to 0.6725 on a central analytic-number-theory target. The full hypothesis remains unresolved. Lamzouri’s separate human follow-up replaces the matrix framework with a Hilbert-space inequality and gives additional unconditional estimates, including a proportion above 88.76% for zeros that are simple or on the critical line (or both). This follow-up is linked context, not a second count of the same AI discovery.
The AI contribution
The source attributes discovery to Claude; the named human authors validated and communicated the argument.
Limitations
The full Riemann hypothesis remains a stronger statement. AIProofWatch has not rerun the Lean project or audited the analytic dependencies. The paper’s authors work at Anthropic, so their validation is not independent checking. Lamzouri gives a different proof of the proportion bound, not a line-by-line audit of Claude’s original proof. His additional results are human work and are not attributed to Claude. AIProofWatch has not audited the follow-up.
Verification evidence
Evidence labels show what supports the claim. Importance rates its impact if correct.
Author claim
Reported theorem and provenance in version 2.
Accessible artifact / proof
Pinned-toolchain project and comparator information are available.
Formal checking
Anthropic reports Lean/comparator checking; AIProofWatch has not run it.
Checker: Anthropic formalization team (reported)
Scope: The project’s statement on simple critical-line zeros, under its declared analytic dependencies.
Basis: Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Correction and publication history
News-led source-context amendment, preserving the existing claim, rating, AI attribution and checking limits. No subscriber alerts.
Read this published revisionEditorial importance reassessment: rate the scoped impact if correct independently from verification. The claim, limitations, sources, and verification evidence are unchanged.
Read this published revisionHistorical seed, researched for the initial catalog. Initial alerting disabled.
Read this published revision