{"schema_version":"source-reader-v1","record":{"source_id":"openai-quasi-rh","versions":[{"work":{"authors":["OpenAI"],"kind":"research_paper","publication":"preprint","publication_note":"Preprint released in the 6 October 2026 collection. The repository’s formalization metadata marks review status unchecked. Recorded here as a proposed result awaiting assessment; formal checking and mathematical faithfulness are separate.","ai_role":"self_reported","ai_note":"OpenAI attributes this collection to an unreleased internal model. The zero-free-region work is an exception to the usual fixed evaluation procedure; the alternate 11/12 writeup was human-edited for readability. Do not infer a public model version or attribute individual GPT-6 submissions to this company release.","artifacts":[{"kind":"pdf","title":"Proposed seven-eighths proof PDF","url":"https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Quasi-Riemann-Hypothesis-September-30-2026/paper.pdf","version":"fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb","assessment":"external_report","note":"Manuscript claims a fixed Re(s) > 7/8 region. Its proof and faithfulness to the formal target have not been independently assessed by OpenMath."},{"kind":"pdf","title":"Alternate eleven-twelfths proof PDF","url":"https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Quasi-Riemann-Hypothesis-October-5-2026/paper2.pdf","version":"fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb","assessment":"external_report","note":"Weaker fixed region Re(s) > 11/12; an alternate argument within the same source family, not a duplicate new RH Problem."},{"kind":"formal_code","title":"OpenAI Lean implementation · pinned commit","url":"https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/OAI/NumberTheory/DirichletL/Nonvanishing.lean","version":"fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb","assessment":"external_report","note":"The formalization catalogue maps actual Mathlib riemannZeta and Dirichlet L-function targets to this file. Comparator target files contain intentional sorry placeholders. No local compilation, axiom audit or statement-faithfulness review is asserted here."},{"kind":"project_notes","title":"Formalization scope · family 003","url":"https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/003.md","version":"fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb","assessment":"external_report","note":"Scope includes zeta, all positive Dirichlet moduli and finite-order Hecke L-functions over Q(√−3); excludes principal poles and later arithmetic applications."},{"kind":"project_notes","title":"Release and review metadata","url":"https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/formalization.yaml","version":"fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb","assessment":"external_report","note":"Metadata declares review.status unchecked for the collection. Exact pin preserves later correction history."}]},"id":"openai-quasi-rh@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb","source_id":"openai-quasi-rh","title":"OpenAI · reported seven-eighths half-plane","owner":"OpenAI","url":"https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Quasi-Riemann-Hypothesis-September-30-2026/README.md","subject_scope":"OpenAI · reported seven-eighths half-plane","revision":"git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb","content_sha256":null,"update_method":"Manual source and revision check; recheck upstream before a new publication.","identifier_policy":"Stable bibliographic identifier and explicit revision; theorem locators belong to source entries.","observed_on":"2026-10-10","source_updated_on":"2026-09-30","rights":"metadata-link","license":"Links and original OpenMath paraphrases only; upstream license governs external files.","terms_url":"https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Quasi-Riemann-Hypothesis-September-30-2026/README.md","attribution":"OpenAI","rights_note":"No upstream full text or code is republished by this record.","check_interval_days":30}],"entries":[{"id":"riemann-hypothesis:rh-openai-seven-eighths:v1","source_version_id":"openai-quasi-rh@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb","item_id":"openai-quasi-rh#rh-openai-seven-eighths","url":"https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Quasi-Riemann-Hypothesis-September-30-2026/README.md","wording":"OpenAI claims a fixed zero-free half-plane Re(s) > 7/8 for zeta and all Dirichlet L-functions.","wording_kind":"paraphrase","locator":"Theorem 1.1; formalization scope family 003; comparator OAI.riemannZeta_ne_zero_of_seven_eighths_lt_re","supersedes":null}],"problems":[{"slug":"riemann-hypothesis","title":"Riemann hypothesis","publication_version":13}],"selected_version_id":"openai-quasi-rh@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb","available_versions":[{"id":"openai-quasi-rh@git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb","revision":"git-fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb","observed_on":"2026-10-10","title":"OpenAI · reported seven-eighths half-plane","publication":"preprint","content_sha256":null,"used_in_current_publications":true}],"usages":[{"id":"source-use-28f3a091897930e66511","entry_id":"riemann-hypothesis:rh-openai-seven-eighths:v1","problem":{"slug":"riemann-hypothesis","title":"Riemann hypothesis","publication_version":13},"kind":"activity","title":"Recent AI-related proposals awaiting assessment","claim":null,"fragment":"activity","assessment":null,"superseded":false,"formalization":null,"update":{"id":"activity-rh-new-ai-proposals","title":"Recent AI-related proposals awaiting assessment","kind":"research_direction","source_entry_ids":["riemann-hypothesis:rh-openai-seven-eighths:v1","riemann-hypothesis:rh-gomila-newman-candidate:v1"],"summary":"OpenAI reports a seven-eighths zero-free half-plane with Lean artifacts; Gomila reports an improved positive Newman upper bound with interval certificates. Each proposed Claim has its own scope and pinned source evidence.","limitation":"These are proposals in this publication, excluded from established progress. No cited source establishes the full classical RH here.","related_claim_ids":["claim-rh-proposed-seven-eighths-half-plane"]}},{"id":"source-use-fa2848f5562647b3f11c","entry_id":"riemann-hypothesis:rh-openai-seven-eighths:v1","problem":{"slug":"riemann-hypothesis","title":"Riemann hypothesis","publication_version":13},"kind":"assessment","title":"Proposed bound · external formalization reported; review unchecked","claim":{"id":"claim-rh-proposed-seven-eighths-half-plane","version":2,"slug":"rh-proposed-seven-eighths-half-plane","title":"Proposed result: a fixed zero-free half-plane Re(s) > 7/8"},"fragment":"claim-rh-proposed-seven-eighths-half-plane","assessment":{"id":"riemann-hypothesis:rh-openai-seven-eighths:report:v1","entry_id":"riemann-hypothesis:rh-openai-seven-eighths:v1","state":"proposed_solution","source_label":"Proposed bound · external formalization reported; review unchecked","scope":"Only the exact statement, domain and revision cited by this Claim; this is not a resolution of classical RH or independent OpenMath expert assessment.","source_date":"2026-09-30","observed_on":"2026-10-10","evidence_url":"https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Quasi-Riemann-Hypothesis-September-30-2026/README.md","supersedes":null},"superseded":false,"formalization":null,"update":null},{"id":"source-use-7167b4d9efd4726f8075","entry_id":"riemann-hypothesis:rh-openai-seven-eighths:v1","problem":{"slug":"riemann-hypothesis","title":"Riemann hypothesis","publication_version":13},"kind":"milestone","title":"OpenAI’s proposed seven-eighths half-plane","claim":null,"fragment":"history","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-87c681d24dbee5e15d65","entry_id":"riemann-hypothesis:rh-openai-seven-eighths:v1","problem":{"slug":"riemann-hypothesis","title":"Riemann hypothesis","publication_version":13},"kind":"question","title":"Riemann hypothesis","claim":null,"fragment":"question","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-12ca9d7ebe01eb036c65","entry_id":"riemann-hypothesis:rh-openai-seven-eighths:v1","problem":{"slug":"riemann-hypothesis","title":"Riemann hypothesis","publication_version":13},"kind":"statement","title":"Proposed result: a fixed zero-free half-plane Re(s) > 7/8","claim":{"id":"claim-rh-proposed-seven-eighths-half-plane","version":2,"slug":"rh-proposed-seven-eighths-half-plane","title":"Proposed result: a fixed zero-free half-plane Re(s) > 7/8"},"fragment":"claim-rh-proposed-seven-eighths-half-plane","assessment":null,"superseded":false,"formalization":null,"update":null}],"linked_entries":[],"linked_sources":[]}}