{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6CNRSL4UX27HWC26DBIMN4HLAT","short_pith_number":"pith:6CNRSL4U","schema_version":"1.0","canonical_sha256":"f09b192f94bebe7b0b5e1850c6f0eb04eeadc591f7045dc76f117323a4945255","source":{"kind":"arxiv","id":"1407.1447","version":1},"attestation_state":"computed","paper":{"title":"On the coincidence of Pascal lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Jaydeep Chipalkatti","submitted_at":"2014-07-06T00:30:08Z","abstract_excerpt":"Let ${\\mathcal K}$ denote a smooth conic in the complex projective plane. Pascal's theorem says that, given six points $A,B,C,D,E,F$ on ${\\mathcal K}$, the three intersection points $AE \\cap BF, AD \\cap CF, BD \\cap CE$ are collinear. This defines the Pascal line of the array $\\left[ \\begin{array}{ccc} A & B & C \\\\ F & E & D \\end{array} \\right]$, and one gets sixty such lines in general by permuting the points. In this paper we consider the variety $\\Psi$ of sextuples $\\{A, \\dots, F\\}$, for which some of these Pascal lines coincide. We show that $\\Psi$ has two irreducible components: a five-dim"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.1447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-06T00:30:08Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"5d3128bcd1781808a2a5a5f5a31d63b32d12891d86ed3b4f5cadf61c98d2ca08","abstract_canon_sha256":"f57e41ece0fd2956889c3267cde3593c618e93da298aca05d391c7e1b6657bf9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:16.570477Z","signature_b64":"YKaNo3thqugZlOq5pwou0UT4XAQE0VdvgYp9UJcRXu+pfZnsvuC2wbKj2cAzxrc69xEO44C+9RZ6QNo0u2hIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f09b192f94bebe7b0b5e1850c6f0eb04eeadc591f7045dc76f117323a4945255","last_reissued_at":"2026-05-18T02:48:16.570003Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:16.570003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the coincidence of Pascal lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Jaydeep Chipalkatti","submitted_at":"2014-07-06T00:30:08Z","abstract_excerpt":"Let ${\\mathcal K}$ denote a smooth conic in the complex projective plane. Pascal's theorem says that, given six points $A,B,C,D,E,F$ on ${\\mathcal K}$, the three intersection points $AE \\cap BF, AD \\cap CF, BD \\cap CE$ are collinear. This defines the Pascal line of the array $\\left[ \\begin{array}{ccc} A & B & C \\\\ F & E & D \\end{array} \\right]$, and one gets sixty such lines in general by permuting the points. In this paper we consider the variety $\\Psi$ of sextuples $\\{A, \\dots, F\\}$, for which some of these Pascal lines coincide. We show that $\\Psi$ has two irreducible components: a five-dim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1447","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.1447","created_at":"2026-05-18T02:48:16.570076+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.1447v1","created_at":"2026-05-18T02:48:16.570076+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1447","created_at":"2026-05-18T02:48:16.570076+00:00"},{"alias_kind":"pith_short_12","alias_value":"6CNRSL4UX27H","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6CNRSL4UX27HWC26","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6CNRSL4U","created_at":"2026-05-18T12:28:16.859392+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6CNRSL4UX27HWC26DBIMN4HLAT","json":"https://pith.science/pith/6CNRSL4UX27HWC26DBIMN4HLAT.json","graph_json":"https://pith.science/api/pith-number/6CNRSL4UX27HWC26DBIMN4HLAT/graph.json","events_json":"https://pith.science/api/pith-number/6CNRSL4UX27HWC26DBIMN4HLAT/events.json","paper":"https://pith.science/paper/6CNRSL4U"},"agent_actions":{"view_html":"https://pith.science/pith/6CNRSL4UX27HWC26DBIMN4HLAT","download_json":"https://pith.science/pith/6CNRSL4UX27HWC26DBIMN4HLAT.json","view_paper":"https://pith.science/paper/6CNRSL4U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.1447&json=true","fetch_graph":"https://pith.science/api/pith-number/6CNRSL4UX27HWC26DBIMN4HLAT/graph.json","fetch_events":"https://pith.science/api/pith-number/6CNRSL4UX27HWC26DBIMN4HLAT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6CNRSL4UX27HWC26DBIMN4HLAT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6CNRSL4UX27HWC26DBIMN4HLAT/action/storage_attestation","attest_author":"https://pith.science/pith/6CNRSL4UX27HWC26DBIMN4HLAT/action/author_attestation","sign_citation":"https://pith.science/pith/6CNRSL4UX27HWC26DBIMN4HLAT/action/citation_signature","submit_replication":"https://pith.science/pith/6CNRSL4UX27HWC26DBIMN4HLAT/action/replication_record"}},"created_at":"2026-05-18T02:48:16.570076+00:00","updated_at":"2026-05-18T02:48:16.570076+00:00"}