{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JCI42KRGMNOY7POBU3OVXNZPHZ","short_pith_number":"pith:JCI42KRG","schema_version":"1.0","canonical_sha256":"4891cd2a26635d8fbdc1a6dd5bb72f3e681c0ca345642535f2725f2a965b0650","source":{"kind":"arxiv","id":"1406.7256","version":2},"attestation_state":"computed","paper":{"title":"Identifiability of 3-Class Jukes-Cantor Mixtures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"q-bio.PE","authors_text":"Colby Long, Seth Sullivant","submitted_at":"2014-06-27T18:09:53Z","abstract_excerpt":"We prove identifiability of the tree parameters of the 3-class Jukes-Cantor mixture model. The proof uses ideas from algebraic statistics, in particular: finding phylogenetic invariants that separate the varieties associated to different triples of trees; computing dimensions of the resulting phylogenetic varieties; and using the disentangling number to reduce to trees with a small number of leaves. Symbolic computation also plays a key role in handling the many different cases and finding relevant phylogenetic invariants."},"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":"1406.7256","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2014-06-27T18:09:53Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"67390bcdf65b012ea5faf97d0ec4a4ce6a487f5d102fb569fdf410897980107b","abstract_canon_sha256":"00b31bd639273554188015940c43f14d432f1abb72a6f94d916b8066563a96cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:31.117499Z","signature_b64":"7VgkX/A2NThYt/fRsnrU2V+xK7szR9tZ/LVuogyQlhp4oD9tFhtjatBzKRCzSnENXCkhjYAyHDACgRlY+TEaDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4891cd2a26635d8fbdc1a6dd5bb72f3e681c0ca345642535f2725f2a965b0650","last_reissued_at":"2026-05-18T02:45:31.116755Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:31.116755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Identifiability of 3-Class Jukes-Cantor Mixtures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"q-bio.PE","authors_text":"Colby Long, Seth Sullivant","submitted_at":"2014-06-27T18:09:53Z","abstract_excerpt":"We prove identifiability of the tree parameters of the 3-class Jukes-Cantor mixture model. The proof uses ideas from algebraic statistics, in particular: finding phylogenetic invariants that separate the varieties associated to different triples of trees; computing dimensions of the resulting phylogenetic varieties; and using the disentangling number to reduce to trees with a small number of leaves. Symbolic computation also plays a key role in handling the many different cases and finding relevant phylogenetic invariants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7256","kind":"arxiv","version":2},"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":"1406.7256","created_at":"2026-05-18T02:45:31.116877+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.7256v2","created_at":"2026-05-18T02:45:31.116877+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7256","created_at":"2026-05-18T02:45:31.116877+00:00"},{"alias_kind":"pith_short_12","alias_value":"JCI42KRGMNOY","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"JCI42KRGMNOY7POB","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"JCI42KRG","created_at":"2026-05-18T12:28:33.132498+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/JCI42KRGMNOY7POBU3OVXNZPHZ","json":"https://pith.science/pith/JCI42KRGMNOY7POBU3OVXNZPHZ.json","graph_json":"https://pith.science/api/pith-number/JCI42KRGMNOY7POBU3OVXNZPHZ/graph.json","events_json":"https://pith.science/api/pith-number/JCI42KRGMNOY7POBU3OVXNZPHZ/events.json","paper":"https://pith.science/paper/JCI42KRG"},"agent_actions":{"view_html":"https://pith.science/pith/JCI42KRGMNOY7POBU3OVXNZPHZ","download_json":"https://pith.science/pith/JCI42KRGMNOY7POBU3OVXNZPHZ.json","view_paper":"https://pith.science/paper/JCI42KRG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.7256&json=true","fetch_graph":"https://pith.science/api/pith-number/JCI42KRGMNOY7POBU3OVXNZPHZ/graph.json","fetch_events":"https://pith.science/api/pith-number/JCI42KRGMNOY7POBU3OVXNZPHZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JCI42KRGMNOY7POBU3OVXNZPHZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JCI42KRGMNOY7POBU3OVXNZPHZ/action/storage_attestation","attest_author":"https://pith.science/pith/JCI42KRGMNOY7POBU3OVXNZPHZ/action/author_attestation","sign_citation":"https://pith.science/pith/JCI42KRGMNOY7POBU3OVXNZPHZ/action/citation_signature","submit_replication":"https://pith.science/pith/JCI42KRGMNOY7POBU3OVXNZPHZ/action/replication_record"}},"created_at":"2026-05-18T02:45:31.116877+00:00","updated_at":"2026-05-18T02:45:31.116877+00:00"}