{"schema_version":"source-reader-v1","record":{"source_id":"sendov-conjecture-digestion","versions":[{"work":{"authors":["Terence Tao"],"kind":"research_paper","publication":"project","publication_note":"Public manuscript or exposition; publication does not imply independent OpenMath review.","ai_role":"self_reported","ai_note":"Terence Tao performed mathematical digestion and simplification with substantial AI assistance; this descends from Mazur’s argument and is not an independent discovery route.","artifacts":[],"published":{"value":"2026-08-12"}},"id":"sendov-conjecture:source:digestion:v1","source_id":"sendov-conjecture-digestion","title":"A digestion of the proof of Sendov’s conjecture","owner":"Terence Tao","url":"https://terrytao.wordpress.com/2026/08/12/a-digestion-of-the-proof-of-sendovs-conjecture/","subject_scope":"A streamlined exposition of Mazur’s argument gives Sendov and the sharper Phelps–Rodriguez conclusion, with its boundary equality cases.","revision":"2026-08-12","content_sha256":null,"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":"2026-08-12","rights":"metadata-link","license":"Original document rights remain with its authors.","terms_url":"https://terrytao.wordpress.com/2026/08/12/a-digestion-of-the-proof-of-sendovs-conjecture/","attribution":"Terence Tao","rights_note":"OpenMath supplies original paraphrases and links; no proof text is republished.","check_interval_days":90}],"entries":[{"id":"sendov-conjecture:entry:digestion:v1","source_version_id":"sendov-conjecture:source:digestion:v1","item_id":"digestion","url":"https://terrytao.wordpress.com/2026/08/12/a-digestion-of-the-proof-of-sendovs-conjecture/","wording":"A streamlined exposition of Mazur’s argument gives Sendov and the sharper Phelps–Rodriguez conclusion, with its boundary equality cases.","wording_kind":"paraphrase","locator":"Conjectures 1–3 and proof, with provenance remarks","supersedes":null}],"problems":[{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8}],"selected_version_id":"sendov-conjecture:source:digestion:v1","available_versions":[{"id":"sendov-conjecture:source:digestion:v1","revision":"2026-08-12","observed_on":"2026-10-13","title":"A digestion of the proof of Sendov’s conjecture","publication":"project","content_sha256":null,"used_in_current_publications":true}],"usages":[{"id":"source-use-6317f3fbc3d150b5010b","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"activity","title":"Discovery, exposition and formalization","claim":null,"fragment":"activity","assessment":null,"superseded":false,"formalization":null,"update":{"id":"sendov-conjecture-credits","title":"Discovery, exposition and formalization","kind":"formalization","source_entry_ids":["sendov-conjecture:entry:mazur:v1","sendov-conjecture:entry:digestion:v1","sendov-conjecture:entry:lean:v1"],"summary":"Mazur and GPT-5.6 Pro supplied the original result; Tao digested its mathematics and directed the second formalization, whose project credits Claude Opus 5.","limitation":"Two formalizations of a descended argument do not automatically constitute two independent mathematical proofs.","related_claim_ids":["claim-sendov-distance-one","claim-sendov-phelps-rodriguez"]}},{"id":"source-use-0d00e5eccdbaa84b074f","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"assessment","title":"Sendov and the sharper form proved in the exposition","claim":{"id":"claim-sendov-phelps-rodriguez","version":2,"slug":"sendov-phelps-rodriguez","title":"Strict distance and the equality exception"},"fragment":"claim-sendov-phelps-rodriguez","assessment":{"id":"sendov-conjecture:report:full:v1","entry_id":"sendov-conjecture:entry:digestion:v1","state":"resolved","source_label":"Sendov and the sharper form proved in the exposition","scope":"All degrees n ≥ 2 with the stated disk assumption.","source_date":null,"observed_on":"2026-10-13","evidence_url":"https://terrytao.wordpress.com/2026/08/12/a-digestion-of-the-proof-of-sendovs-conjecture/","supersedes":null},"superseded":false,"formalization":null,"update":null},{"id":"source-use-62f3668f2c4065a849ad","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"assessment","title":"Sendov and the sharper form proved in the exposition","claim":{"id":"claim-sendov-sharp-radius-example","version":2,"slug":"sendov-sharp-radius-example","title":"Why the radius one is sharp"},"fragment":"claim-sendov-sharp-radius-example","assessment":{"id":"sendov-conjecture:report:full:v1","entry_id":"sendov-conjecture:entry:digestion:v1","state":"resolved","source_label":"Sendov and the sharper form proved in the exposition","scope":"All degrees n ≥ 2 with the stated disk assumption.","source_date":null,"observed_on":"2026-10-13","evidence_url":"https://terrytao.wordpress.com/2026/08/12/a-digestion-of-the-proof-of-sendovs-conjecture/","supersedes":null},"superseded":false,"formalization":null,"update":null},{"id":"source-use-baed77a2b38a0da271e9","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"assessment","title":"Sendov and the sharper form proved in the exposition","claim":{"id":"claim-sendov-distance-one","version":2,"slug":"sendov-distance-one","title":"A critical point within distance one"},"fragment":"claim-sendov-distance-one","assessment":{"id":"sendov-conjecture:report:full:v1","entry_id":"sendov-conjecture:entry:digestion:v1","state":"resolved","source_label":"Sendov and the sharper form proved in the exposition","scope":"All degrees n ≥ 2 with the stated disk assumption.","source_date":null,"observed_on":"2026-10-13","evidence_url":"https://terrytao.wordpress.com/2026/08/12/a-digestion-of-the-proof-of-sendovs-conjecture/","supersedes":null},"superseded":false,"formalization":null,"update":null},{"id":"source-use-33372d72e41f2a8b0156","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"definition","title":"Critical point","claim":null,"fragment":"question","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-12c11f5ec512faae9cb1","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"formalization","title":"Lean: the sharp Phelps–Rodriguez form","claim":{"id":"claim-sendov-phelps-rodriguez","version":2,"slug":"sendov-phelps-rodriguez","title":"Strict distance and the equality exception"},"fragment":"claim-sendov-phelps-rodriguez","assessment":null,"superseded":false,"formalization":{"title":"Lean: the sharp Phelps–Rodriguez form","url":"https://github.com/teorth/sendov/blob/1ddea92d89f951a0a7cbbffa6c267cf7e6640b1d/Sendov/Conjecture.lean","note":"Source-reported complete, including the equality classification. Independent OpenMath execution and review remain pending.","target":{"id":"claim-sendov-phelps-rodriguez","version":2},"proof_status":"reported_complete","source_entry_ids":["sendov-conjecture:entry:digestion:v1","sendov-conjecture:entry:lean:v1"],"declaration":"Sendov.phelps_rodriguez","source_commit":"1ddea92d89f951a0a7cbbffa6c267cf7e6640b1d","alignment":"staff_linked","checked_on":"2026-10-13"},"update":null},{"id":"source-use-411cbc5686f96d9bfd02","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"formalization","title":"Lean: Sendov for every degree","claim":{"id":"claim-sendov-distance-one","version":2,"slug":"sendov-distance-one","title":"A critical point within distance one"},"fragment":"claim-sendov-distance-one","assessment":null,"superseded":false,"formalization":{"title":"Lean: Sendov for every degree","url":"https://github.com/teorth/sendov/blob/1ddea92d89f951a0a7cbbffa6c267cf7e6640b1d/Sendov/Conjecture.lean","note":"Source-reported complete. The separate Challenge file contains deliberate statement placeholders; the project reports no holes in the proof endpoint.","target":{"id":"claim-sendov-distance-one","version":2},"proof_status":"reported_complete","source_entry_ids":["sendov-conjecture:entry:mazur:v1","sendov-conjecture:entry:digestion:v1","sendov-conjecture:entry:lean:v1"],"declaration":"Sendov.sendov","source_commit":"1ddea92d89f951a0a7cbbffa6c267cf7e6640b1d","alignment":"staff_linked","checked_on":"2026-10-13"},"update":null},{"id":"source-use-04b3d750e6965709e00b","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"milestone","title":"A human-readable proof and sharper conclusion","claim":null,"fragment":"history","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-342065395623693f62f8","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"milestone","title":"Boundary case and equality classification","claim":null,"fragment":"history","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-3b1b6491affce5c4ff1a","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"milestone","title":"Earlier partial results","claim":null,"fragment":"history","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-b6cd8678104d1d76d1c6","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"question","title":"Sendov’s conjecture","claim":null,"fragment":"question","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-fef840d32e77ded43656","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"reading","title":"Read the setting and notation before comparing the results.","claim":null,"fragment":"provenance","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-118470fe94beee28dd8b","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"scope","title":"A critical point within distance one","claim":{"id":"claim-sendov-distance-one","version":2,"slug":"sendov-distance-one","title":"A critical point within distance one"},"fragment":"claim-sendov-distance-one","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-1cfe711555ffaaf5d57d","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"scope","title":"Why the radius one is sharp","claim":{"id":"claim-sendov-sharp-radius-example","version":2,"slug":"sendov-sharp-radius-example","title":"Why the radius one is sharp"},"fragment":"claim-sendov-sharp-radius-example","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-60ea2b1840147fedf621","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"scope","title":"Strict distance and the equality exception","claim":{"id":"claim-sendov-phelps-rodriguez","version":2,"slug":"sendov-phelps-rodriguez","title":"Strict distance and the equality exception"},"fragment":"claim-sendov-phelps-rodriguez","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-3996e3b980e3ad105c00","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"statement","title":"Strict distance and the equality exception","claim":{"id":"claim-sendov-phelps-rodriguez","version":2,"slug":"sendov-phelps-rodriguez","title":"Strict distance and the equality exception"},"fragment":"claim-sendov-phelps-rodriguez","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-c9b3671b898cc2c84e16","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"statement","title":"A critical point within distance one","claim":{"id":"claim-sendov-distance-one","version":2,"slug":"sendov-distance-one","title":"A critical point within distance one"},"fragment":"claim-sendov-distance-one","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-d70bd94f2d02a8b2e5fa","entry_id":"sendov-conjecture:entry:digestion:v1","problem":{"slug":"sendov-conjecture","title":"Sendov’s conjecture","publication_version":8},"kind":"statement","title":"Why the radius one is sharp","claim":{"id":"claim-sendov-sharp-radius-example","version":2,"slug":"sendov-sharp-radius-example","title":"Why the radius one is sharp"},"fragment":"claim-sendov-sharp-radius-example","assessment":null,"superseded":false,"formalization":null,"update":null}],"linked_entries":[{"id":"sendov-conjecture:entry:digestion:v1","source_version_id":"sendov-conjecture:source:digestion:v1","item_id":"digestion","url":"https://terrytao.wordpress.com/2026/08/12/a-digestion-of-the-proof-of-sendovs-conjecture/","wording":"A streamlined exposition of Mazur’s argument gives Sendov and the sharper Phelps–Rodriguez conclusion, with its boundary equality cases.","wording_kind":"paraphrase","locator":"Conjectures 1–3 and proof, with provenance remarks","supersedes":null},{"id":"sendov-conjecture:entry:lean:v1","source_version_id":"sendov-conjecture:source:lean:v1","item_id":"lean","url":"https://github.com/teorth/sendov/tree/1ddea92d89f951a0a7cbbffa6c267cf7e6640b1d","wording":"The pinned public source states full Sendov and Phelps–Rodriguez endpoints and reports only the standard Lean logical axioms for their proofs.","wording_kind":"paraphrase","locator":"README provenance and trust; Sendov/Conjecture.lean","supersedes":null},{"id":"sendov-conjecture:entry:mazur:v1","source_version_id":"sendov-conjecture:source:mazur:v1","item_id":"mazur","url":"https://www.proofatlas.ai/papers/sendov-conjecture/SENDOV_CONJECTURE_PROOF_AUGUST_5_2026.pdf","wording":"A directed AI workflow reports a proof of Sendov for every degree at least two; the original proof and formalization preceded Tao’s exposition.","wording_kind":"paraphrase","locator":"Original proof dated 5 August 2026","supersedes":null}],"linked_sources":[{"work":{"authors":["Terence Tao"],"kind":"research_paper","publication":"project","publication_note":"Public manuscript or exposition; publication does not imply independent OpenMath review.","ai_role":"self_reported","ai_note":"Terence Tao performed mathematical digestion and simplification with substantial AI assistance; this descends from Mazur’s argument and is not an independent discovery route.","artifacts":[],"published":{"value":"2026-08-12"}},"id":"sendov-conjecture:source:digestion:v1","source_id":"sendov-conjecture-digestion","title":"A digestion of the proof of Sendov’s conjecture","owner":"Terence Tao","url":"https://terrytao.wordpress.com/2026/08/12/a-digestion-of-the-proof-of-sendovs-conjecture/","subject_scope":"A streamlined exposition of Mazur’s argument gives Sendov and the sharper Phelps–Rodriguez conclusion, with its boundary equality cases.","revision":"2026-08-12","content_sha256":null,"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":"2026-08-12","rights":"metadata-link","license":"Original document rights remain with its authors.","terms_url":"https://terrytao.wordpress.com/2026/08/12/a-digestion-of-the-proof-of-sendovs-conjecture/","attribution":"Terence Tao","rights_note":"OpenMath supplies original paraphrases and links; no proof text is republished.","check_interval_days":90},{"work":{"authors":["Terence Tao","teorth/sendov project"],"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 reports Claude Opus 5 wrote essentially all Lean source under the author’s direction and review; this is a second formalization of the same mathematical argument.","artifacts":[{"kind":"formal_code","title":"Sendov and Phelps–Rodriguez in Lean — pinned source","url":"https://github.com/teorth/sendov/tree/1ddea92d89f951a0a7cbbffa6c267cf7e6640b1d","version":"1ddea92d89f951a0a7cbbffa6c267cf7e6640b1d","assessment":"not_executed","note":"Public source inspected for statement and assumptions; this proof project has not been executed by OpenMath."}],"published":{"value":"2026-08-19"}},"id":"sendov-conjecture:source:lean:v1","source_id":"sendov-conjecture-lean","title":"Sendov and Phelps–Rodriguez in Lean","owner":"Terence Tao, teorth/sendov project","url":"https://github.com/teorth/sendov/tree/1ddea92d89f951a0a7cbbffa6c267cf7e6640b1d","subject_scope":"The pinned public source states full Sendov and Phelps–Rodriguez endpoints and reports only the standard Lean logical axioms for their proofs.","revision":"1ddea92d89f951a0a7cbbffa6c267cf7e6640b1d","content_sha256":"f24582c2d2fe024e762656a7d175e1743e65fb034acce2fb2a43ab2b5cfe3229","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":"2026-08-19","rights":"metadata-link","license":"Original document rights remain with its authors.","terms_url":"https://github.com/teorth/sendov/tree/1ddea92d89f951a0a7cbbffa6c267cf7e6640b1d","attribution":"Terence Tao, teorth/sendov project","rights_note":"OpenMath supplies original paraphrases and links; no proof text is republished.","check_interval_days":90},{"work":{"authors":["Lech Mazur"],"kind":"research_paper","publication":"preprint","publication_note":"Public manuscript or exposition; publication does not imply independent OpenMath review.","ai_role":"self_reported","ai_note":"Lech Mazur directed GPT-5.6 Pro discovery and formal work; mathematical direction, model work and later exposition are distinct contributions.","artifacts":[],"published":{"value":"2026-08-05"}},"id":"sendov-conjecture:source:mazur:v1","source_id":"sendov-conjecture-mazur","title":"Sendov conjecture: original proof","owner":"Lech Mazur","url":"https://www.proofatlas.ai/papers/sendov-conjecture/SENDOV_CONJECTURE_PROOF_AUGUST_5_2026.pdf","subject_scope":"A directed AI workflow reports a proof of Sendov for every degree at least two; the original proof and formalization preceded Tao’s exposition.","revision":"2026-08-05","content_sha256":null,"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":"2026-08-05","rights":"metadata-link","license":"Original document rights remain with its authors.","terms_url":"https://www.proofatlas.ai/papers/sendov-conjecture/SENDOV_CONJECTURE_PROOF_AUGUST_5_2026.pdf","attribution":"Lech Mazur","rights_note":"OpenMath supplies original paraphrases and links; no proof text is republished.","check_interval_days":90}]}}