{"schema_version":"source-reader-v1","record":{"source_id":"prime-gaps-186-lean","versions":[{"work":{"authors":["OpenAI","PrimeGaps186 contributors"],"kind":"research_project","publication":"project","publication_note":"Public formal source; build and independent mathematical review are separate checks.","ai_role":"self_reported","ai_note":"The project is an OpenAI formal development. Its explicit assumptions and certificate work are recorded separately from an unconditional mathematical improvement.","artifacts":[{"kind":"formal_code","title":"Prime gaps at most 186: a conditional Lean development — pinned source","url":"https://github.com/openai/PrimeGaps186/tree/61340d0b74163003b32756bb16e91d9209a5e330","version":"61340d0b74163003b32756bb16e91d9209a5e330","assessment":"not_executed","note":"Public source inspected for statement and assumptions; this proof project has not been executed by OpenMath."}],"published":{"value":"2026-09-02"}},"id":"prime-gaps:source:186-lean:v1","source_id":"prime-gaps-186-lean","title":"Prime gaps at most 186: a conditional Lean development","owner":"OpenAI, PrimeGaps186 contributors","url":"https://github.com/openai/PrimeGaps186/tree/61340d0b74163003b32756bb16e91d9209a5e330","subject_scope":"The endpoint derives a gap bound of 186 from two unproved-in-Lean exponential-sum estimates and an unproved-in-Lean physical integral input. A separate numerical certificate does not discharge those axioms.","revision":"61340d0b74163003b32756bb16e91d9209a5e330","content_sha256":"be1e3ec09817391ee634f23c624b498fc0e5563f1c30ad1fbfadf57ae4bacb3b","update_method":"Source comparison followed by a new immutable curation revision.","identifier_policy":"Stable source and entry identities; changed wording receives a new version.","observed_on":"2026-10-13","source_updated_on":"2026-09-02","rights":"metadata-link","license":"Original document rights remain with its authors.","terms_url":"https://github.com/openai/PrimeGaps186/tree/61340d0b74163003b32756bb16e91d9209a5e330","attribution":"OpenAI, PrimeGaps186 contributors","rights_note":"OpenMath supplies original paraphrases and links; no proof text is republished.","check_interval_days":90}],"entries":[{"id":"prime-gaps:entry:186-lean:v1","source_version_id":"prime-gaps:source:186-lean:v1","item_id":"186-lean","url":"https://github.com/openai/PrimeGaps186/tree/61340d0b74163003b32756bb16e91d9209a5e330","wording":"The endpoint derives a gap bound of 186 from two unproved-in-Lean exponential-sum estimates and an unproved-in-Lean physical integral input. A separate numerical certificate does not discharge those axioms.","wording_kind":"paraphrase","locator":"README input axioms and verification; PrimeGaps186.lean","supersedes":null}],"problems":[{"slug":"prime-gaps","title":"How small can prime gaps be?","publication_version":7}],"selected_version_id":"prime-gaps:source:186-lean:v1","available_versions":[{"id":"prime-gaps:source:186-lean:v1","revision":"61340d0b74163003b32756bb16e91d9209a5e330","observed_on":"2026-10-13","title":"Prime gaps at most 186: a conditional Lean development","publication":"project","content_sha256":"be1e3ec09817391ee634f23c624b498fc0e5563f1c30ad1fbfadf57ae4bacb3b","used_in_current_publications":true}],"usages":[{"id":"source-use-87423533d7490ac02b2a","entry_id":"prime-gaps:entry:186-lean:v1","problem":{"slug":"prime-gaps","title":"How small can prime gaps be?","publication_version":7},"kind":"activity","title":"The 186 numerical certificate and Lean assumptions","claim":null,"fragment":"activity","assessment":null,"superseded":false,"formalization":null,"update":{"id":"prime-gaps-186-certificate","title":"The 186 numerical certificate and Lean assumptions","kind":"computation","source_entry_ids":["prime-gaps:entry:186-lean:v1"],"summary":"The numerical program and the conditional Lean development are distinct artifacts with different checking boundaries.","limitation":"A passing numerical receipt does not discharge the three Lean input axioms.","related_claim_ids":["claim-prime-gaps-186-conditional"]}},{"id":"source-use-8345512e88ea4f46b57f","entry_id":"prime-gaps:entry:186-lean:v1","problem":{"slug":"prime-gaps","title":"How small can prime gaps be?","publication_version":7},"kind":"assessment","title":"Conditional formal endpoint for 186","claim":{"id":"claim-prime-gaps-186-conditional","version":3,"slug":"prime-gaps-186-conditional","title":"A gap bound of 186 from explicit input assumptions"},"fragment":"claim-prime-gaps-186-conditional","assessment":{"id":"prime-gaps:report:186-conditional:v1","entry_id":"prime-gaps:entry:186-lean:v1","state":"resolved","source_label":"Conditional formal endpoint for 186","scope":"The implication from the three stated input axioms.","source_date":null,"observed_on":"2026-10-13","evidence_url":"https://github.com/openai/PrimeGaps186/tree/61340d0b74163003b32756bb16e91d9209a5e330","supersedes":null},"superseded":false,"formalization":null,"update":null},{"id":"source-use-ef2d9b494f3f90b0a079","entry_id":"prime-gaps:entry:186-lean:v1","problem":{"slug":"prime-gaps","title":"How small can prime gaps be?","publication_version":7},"kind":"bound","title":"H₁","claim":{"id":"claim-prime-gaps-186-conditional","version":3,"slug":"prime-gaps-186-conditional","title":"A gap bound of 186 from explicit input assumptions"},"fragment":"claim-prime-gaps-186-conditional","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-10875d4350a82d02f8f4","entry_id":"prime-gaps:entry:186-lean:v1","problem":{"slug":"prime-gaps","title":"How small can prime gaps be?","publication_version":7},"kind":"formalization","title":"Lean: 186 with three input axioms","claim":{"id":"claim-prime-gaps-186-conditional","version":3,"slug":"prime-gaps-186-conditional","title":"A gap bound of 186 from explicit input assumptions"},"fragment":"claim-prime-gaps-186-conditional","assessment":null,"superseded":false,"formalization":{"title":"Lean: 186 with three input axioms","url":"https://github.com/openai/PrimeGaps186/blob/61340d0b74163003b32756bb16e91d9209a5e330/PrimeGaps186.lean","note":"Complete as a conditional deduction. The formal input names are PrimeGap186.kloosterman3_bound, PrimeGap186.kloosterman2_correlation_bound and PrimeGap186.physical_integral_bounds; they remain assumptions, not discharged proof obligations.","target":{"id":"claim-prime-gaps-186-conditional","version":3},"proof_status":"reported_complete","source_entry_ids":["prime-gaps:entry:186-lean:v1"],"declaration":"PrimeGap186.primeGapLiminf_le_186","source_commit":"61340d0b74163003b32756bb16e91d9209a5e330","alignment":"staff_linked","checked_on":"2026-10-13"},"update":null},{"id":"source-use-7bc09830b318dd1d399b","entry_id":"prime-gaps:entry:186-lean:v1","problem":{"slug":"prime-gaps","title":"How small can prime gaps be?","publication_version":7},"kind":"milestone","title":"A conditional formal deduction for 186","claim":null,"fragment":"history","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-37ae90bb79557598c624","entry_id":"prime-gaps:entry:186-lean:v1","problem":{"slug":"prime-gaps","title":"How small can prime gaps be?","publication_version":7},"kind":"question","title":"How small can prime gaps be?","claim":null,"fragment":"question","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-d130c5950753c2980a56","entry_id":"prime-gaps:entry:186-lean:v1","problem":{"slug":"prime-gaps","title":"How small can prime gaps be?","publication_version":7},"kind":"reading","title":"Inspect the formal statement, assumptions and reported checks.","claim":null,"fragment":"provenance","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-a35a810b11f2bdedb6f0","entry_id":"prime-gaps:entry:186-lean:v1","problem":{"slug":"prime-gaps","title":"How small can prime gaps be?","publication_version":7},"kind":"statement","title":"A gap bound of 186 from explicit input assumptions","claim":{"id":"claim-prime-gaps-186-conditional","version":3,"slug":"prime-gaps-186-conditional","title":"A gap bound of 186 from explicit input assumptions"},"fragment":"claim-prime-gaps-186-conditional","assessment":null,"superseded":false,"formalization":null,"update":null}],"linked_entries":[{"id":"prime-gaps:entry:186-lean:v1","source_version_id":"prime-gaps:source:186-lean:v1","item_id":"186-lean","url":"https://github.com/openai/PrimeGaps186/tree/61340d0b74163003b32756bb16e91d9209a5e330","wording":"The endpoint derives a gap bound of 186 from two unproved-in-Lean exponential-sum estimates and an unproved-in-Lean physical integral input. A separate numerical certificate does not discharge those axioms.","wording_kind":"paraphrase","locator":"README input axioms and verification; PrimeGaps186.lean","supersedes":null}],"linked_sources":[{"work":{"authors":["OpenAI","PrimeGaps186 contributors"],"kind":"research_project","publication":"project","publication_note":"Public formal source; build and independent mathematical review are separate checks.","ai_role":"self_reported","ai_note":"The project is an OpenAI formal development. Its explicit assumptions and certificate work are recorded separately from an unconditional mathematical improvement.","artifacts":[{"kind":"formal_code","title":"Prime gaps at most 186: a conditional Lean development — pinned source","url":"https://github.com/openai/PrimeGaps186/tree/61340d0b74163003b32756bb16e91d9209a5e330","version":"61340d0b74163003b32756bb16e91d9209a5e330","assessment":"not_executed","note":"Public source inspected for statement and assumptions; this proof project has not been executed by OpenMath."}],"published":{"value":"2026-09-02"}},"id":"prime-gaps:source:186-lean:v1","source_id":"prime-gaps-186-lean","title":"Prime gaps at most 186: a conditional Lean development","owner":"OpenAI, PrimeGaps186 contributors","url":"https://github.com/openai/PrimeGaps186/tree/61340d0b74163003b32756bb16e91d9209a5e330","subject_scope":"The endpoint derives a gap bound of 186 from two unproved-in-Lean exponential-sum estimates and an unproved-in-Lean physical integral input. A separate numerical certificate does not discharge those axioms.","revision":"61340d0b74163003b32756bb16e91d9209a5e330","content_sha256":"be1e3ec09817391ee634f23c624b498fc0e5563f1c30ad1fbfadf57ae4bacb3b","update_method":"Source comparison followed by a new immutable curation revision.","identifier_policy":"Stable source and entry identities; changed wording receives a new version.","observed_on":"2026-10-13","source_updated_on":"2026-09-02","rights":"metadata-link","license":"Original document rights remain with its authors.","terms_url":"https://github.com/openai/PrimeGaps186/tree/61340d0b74163003b32756bb16e91d9209a5e330","attribution":"OpenAI, PrimeGaps186 contributors","rights_note":"OpenMath supplies original paraphrases and links; no proof text is republished.","check_interval_days":90}]}}