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The Proportion of Zeta Zeros on the Critical Line
An unconditional record, not a resolution: the Riemann hypothesis is untouched, and Anthropic states it does not expect these techniques to lead to a proof of it. The paper is explicit that these are lower bounds only - the remaining third of the zeros are not shown to be off the line, merely not reached by the certificate. What it does settle is a question that was posed. Goldston and Suriajaya had reduced Montgomery's conditional to a single obstruction, the termwise positivity that fails for zeros off the line, and asked what would follow without it. Theorem A replaces that positivity with a rank-trace inequality on a finite compression of Weil's Hermitian form, with Sylvester's law of inertia handling off-line pairs; reading the negative index of truncations as a count of off-line pairs is Bombieri's device. The paper also proves the bound sharp for this route: improving on this way would need pair-correlation information beyond Fourier support 1.
Exact FrontierDelta
proved→proved
Scope and record
Occurred: Oct 29, 2026
Delta type: REGISTRY REVISION
Assumptions: VibeMathed verification: lean-checked. Publication: preprint. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: The Proportion of Zeta Zeros on the Critical Line · Zeta zeros on the line
Confidence: Not scored
Registry verification: lean checked · preprint · partial
Attribution
VibeMathed
registry · event recorded by
Claude (unreleased research version)
model · ai model contributor · Anthropic
Jarred Sumner
human · human collaborator
Levent Alpöge
human · human collaborator
Ralph Furman
human · human collaborator
Eric Easley
human · human collaborator
Artifacts and verifiers
Compute record
No linked compute attempts recorded.
Lineage and corrections
Corrects The Proportion of Zeta Zeros on the Critical Line →
Supersedes The Proportion of Zeta Zeros on the Critical Line →
The Proportion of Zeta Zeros on the Critical Line evidence for this event
Annotated subagent transcripts evidence for this event
This event attributed to Jarred Sumner
Anthropic's announcement evidence for this event
How the argument was found: Claude's account of its own two runs evidence for this event
The Proportion of Zeta Zeros on the Critical Line parent of this event
This event attributed to Claude (unreleased research version)
An unconditional record, not a resolution: the Riemann hypothesis is untouched, and Anthropic states it does not expect these techniques to lead to a proof of it. The paper is explicit that these are lower bounds only - the remaining third of the zeros are not shown to be off the line, merely not reached by the certificate. What it does settle is a question that was posed. Goldston and Suriajaya had reduced Montgomery's conditional to a single obstruction, the termwise positivity that fails for zeros off the line, and asked what would follow without it. Theorem A replaces that positivity with a rank-trace inequality on a finite compression of Weil's Hermitian form, with Sylvester's law of inertia handling off-line pairs; reading the negative index of truncations as a count of off-line pairs is Bombieri's device. The paper also proves the bound sharp for this route: improving on this way would need pair-correlation information beyond Fourier support 1. parent of this event
VibeMathed record: The Proportion of Zeta Zeros on the Critical Line evidence for this event
This event attributed to Eric Easley
This event attributed to Ralph Furman
The Anthropic PDF the entry was first written from, before the arXiv version evidence for this event
Lean repository - audited at tag v1.0; comparator statements under comparator/ evidence for this event
Anthropic's informal note stating the proof concisely evidence for this event
This event attributed to Levent Alpöge
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