{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:4WZV3HPPQB73B7XJSEGSVH3NDB","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":"6baa82a6d7e8f8fa9dbf2f0c8969a8a1dda23bad23619eaf29e318a77576d125","cross_cats_sorted":["cs.CV","cs.DM","math.ST","physics.data-an","q-bio.QM","stat.TH"],"license":"","primary_cat":"cs.DS","submitted_at":"2006-06-11T16:05:51Z","title_canon_sha256":"1b8816ba1a232c18dbfcdd62b8cda076bb0269eb74668a98f279dd938fcc69bc"},"schema_version":"1.0","source":{"id":"cs/0606048","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0606048","created_at":"2026-05-18T04:08:54Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0606048v1","created_at":"2026-05-18T04:08:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0606048","created_at":"2026-05-18T04:08:54Z"},{"alias_kind":"pith_short_12","alias_value":"4WZV3HPPQB73","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"4WZV3HPPQB73B7XJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"4WZV3HPP","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:5f9cd350ea1e65738cac999e017bb3a2ac3580c09548b775cc5a3580f3801816","target":"graph","created_at":"2026-05-18T04:08:54Z","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 consider the problem of constructing an an optimal-weight tree from the 3*(n choose 4) weighted quartet topologies on n objects, where optimality means that the summed weight of the embedded quartet topologiesis optimal (so it can be the case that the optimal tree embeds all quartets as non-optimal topologies). We present a heuristic for reconstructing the optimal-weight tree, and a canonical manner to derive the quartet-topology weights from a given distance matrix. The method repeatedly transforms a bifurcating tree, with all objects involved as leaves, achieving a monotonic approximation","authors_text":"Paul M.B. Vitanyi, Rudi Cilibrasi","cross_cats":["cs.CV","cs.DM","math.ST","physics.data-an","q-bio.QM","stat.TH"],"headline":"","license":"","primary_cat":"cs.DS","submitted_at":"2006-06-11T16:05:51Z","title":"A New Quartet Tree Heuristic for Hierarchical Clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0606048","kind":"arxiv","version":1},"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":"sha256:82cae8ccf5785fcef6498ed7c7aa768d6909ac4c6d09d80cf51402ea301bf413","target":"record","created_at":"2026-05-18T04:08:54Z","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":"6baa82a6d7e8f8fa9dbf2f0c8969a8a1dda23bad23619eaf29e318a77576d125","cross_cats_sorted":["cs.CV","cs.DM","math.ST","physics.data-an","q-bio.QM","stat.TH"],"license":"","primary_cat":"cs.DS","submitted_at":"2006-06-11T16:05:51Z","title_canon_sha256":"1b8816ba1a232c18dbfcdd62b8cda076bb0269eb74668a98f279dd938fcc69bc"},"schema_version":"1.0","source":{"id":"cs/0606048","kind":"arxiv","version":1}},"canonical_sha256":"e5b35d9def807fb0fee9910d2a9f6d1868822bacd6f487911bbbdfe235a8a26a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5b35d9def807fb0fee9910d2a9f6d1868822bacd6f487911bbbdfe235a8a26a","first_computed_at":"2026-05-18T04:08:54.047938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:54.047938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cS+qo2JqkwH0/Ax0E4R0Th5nawOI0O6UOu97Kn2epoHNxC0SWZWIwLdIbVuJiEKAgbB0wYaDSp1nI5Zw/n2+Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:54.048673Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0606048","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82cae8ccf5785fcef6498ed7c7aa768d6909ac4c6d09d80cf51402ea301bf413","sha256:5f9cd350ea1e65738cac999e017bb3a2ac3580c09548b775cc5a3580f3801816"],"state_sha256":"0be88663c0e59425e0339f7aadf38ef3abf21e286d4b7853a53d386ca7d2747e"}