{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XVOPQFODVZIWYVJ7TEFFV7X74Z","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8015d6d942fa220a7bb30ab23104c5e4e9ac411d1a60ab2b91e62e8f8dffb00a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2014-05-10T19:33:29Z","title_canon_sha256":"31e5d20141b8740e7317de5b0b2f7de7f2193628507a74ee536835db9117884e"},"schema_version":"1.0","source":{"id":"1405.2464","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2464","created_at":"2026-05-18T02:23:27Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2464v2","created_at":"2026-05-18T02:23:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2464","created_at":"2026-05-18T02:23:27Z"},{"alias_kind":"pith_short_12","alias_value":"XVOPQFODVZIW","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XVOPQFODVZIWYVJ7","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XVOPQFOD","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:42bec573b972891bd559adda266804078d867c6f37794a764bc87375d7812260","target":"graph","created_at":"2026-05-18T02:23:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We apply classical quartet techniques to the problem of phylogenetic decisiveness and find a value $k$ such that all collections of at least $k$ quartets are decisive. Moreover, we prove that this bound is optimal and give a lower-bound on the probability that a collection of quartets is decisive.","authors_text":"Emili Moan, Joseph Rusinko","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2014-05-10T19:33:29Z","title":"Combinatorics of Linked Systems of Quartet Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2464","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:76da06f6818416893c1fe58e3bc4aa54a8e422232e548fe5d4a273c16ef7ed13","target":"record","created_at":"2026-05-18T02:23:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8015d6d942fa220a7bb30ab23104c5e4e9ac411d1a60ab2b91e62e8f8dffb00a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2014-05-10T19:33:29Z","title_canon_sha256":"31e5d20141b8740e7317de5b0b2f7de7f2193628507a74ee536835db9117884e"},"schema_version":"1.0","source":{"id":"1405.2464","kind":"arxiv","version":2}},"canonical_sha256":"bd5cf815c3ae516c553f990a5afeffe66da70ecdebdcb3117edac3399c2f5b99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd5cf815c3ae516c553f990a5afeffe66da70ecdebdcb3117edac3399c2f5b99","first_computed_at":"2026-05-18T02:23:27.151619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:27.151619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CkVN/0CKY+n/FACbw+2t2x4Kr7KegzMZ+yqb64hw6MjeHRFXy7bZalgaWJdpDjR5Eax5gmFSfSJfcrGW9oUgAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:27.152243Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2464","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76da06f6818416893c1fe58e3bc4aa54a8e422232e548fe5d4a273c16ef7ed13","sha256:42bec573b972891bd559adda266804078d867c6f37794a764bc87375d7812260"],"state_sha256":"50618a13bb4af05c391f8db1bfeeefebe5b14c12701d7621772a1f16a91df450"}