{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:K7ZE3SPFCCKTDLPZZDGCIDSUXH","short_pith_number":"pith:K7ZE3SPF","schema_version":"1.0","canonical_sha256":"57f24dc9e5109531adf9c8cc240e54b9e9fe3d960425b94acd0d5c5424388f38","source":{"kind":"arxiv","id":"1201.5168","version":5},"attestation_state":"computed","paper":{"title":"The maximum agreement subtree problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bhalchandra D. Thatte, Daniel M. Martin","submitted_at":"2012-01-25T00:59:43Z","abstract_excerpt":"In this paper we investigate an extremal problem on binary phylogenetic trees. Given two such trees $T_1$ and $T_2$, both with leaf-set ${1,2,...,n}$, we are interested in the size of the largest subset $S \\subseteq {1,2,...,n}$ of leaves in a common subtree of $T_1$ and $T_2$. We show that any two binary phylogenetic trees have a common subtree on $\\Omega(\\sqrt{\\log{n}})$ leaves, thus improving on the previously known bound of $\\Omega(\\log\\log n)$ due to M. Steel and L. Szekely. To achieve this improved bound, we first consider two special cases of the problem: when one of the trees is balanc"},"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":"1201.5168","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-25T00:59:43Z","cross_cats_sorted":[],"title_canon_sha256":"7e5d4491895300b8311344a0e30ae950ae512d593ea83776931f96b923e6747a","abstract_canon_sha256":"7b286cf0a5712158b8ee2a96119197fef09fa8959499f4f95c79d90b70ae2234"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:11.916512Z","signature_b64":"IcCSrspn/DlpsOEUGAUmaiTyowD5LDPM+DhBAUrdRyi4naXJML0sAKhu+JVkk31wjjVJytp/rHG1ypgS4/H/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57f24dc9e5109531adf9c8cc240e54b9e9fe3d960425b94acd0d5c5424388f38","last_reissued_at":"2026-05-18T03:33:11.915784Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:11.915784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The maximum agreement subtree problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bhalchandra D. Thatte, Daniel M. Martin","submitted_at":"2012-01-25T00:59:43Z","abstract_excerpt":"In this paper we investigate an extremal problem on binary phylogenetic trees. Given two such trees $T_1$ and $T_2$, both with leaf-set ${1,2,...,n}$, we are interested in the size of the largest subset $S \\subseteq {1,2,...,n}$ of leaves in a common subtree of $T_1$ and $T_2$. We show that any two binary phylogenetic trees have a common subtree on $\\Omega(\\sqrt{\\log{n}})$ leaves, thus improving on the previously known bound of $\\Omega(\\log\\log n)$ due to M. Steel and L. Szekely. To achieve this improved bound, we first consider two special cases of the problem: when one of the trees is balanc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5168","kind":"arxiv","version":5},"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":"1201.5168","created_at":"2026-05-18T03:33:11.915907+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.5168v5","created_at":"2026-05-18T03:33:11.915907+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5168","created_at":"2026-05-18T03:33:11.915907+00:00"},{"alias_kind":"pith_short_12","alias_value":"K7ZE3SPFCCKT","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"K7ZE3SPFCCKTDLPZ","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"K7ZE3SPF","created_at":"2026-05-18T12:27:11.947152+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/K7ZE3SPFCCKTDLPZZDGCIDSUXH","json":"https://pith.science/pith/K7ZE3SPFCCKTDLPZZDGCIDSUXH.json","graph_json":"https://pith.science/api/pith-number/K7ZE3SPFCCKTDLPZZDGCIDSUXH/graph.json","events_json":"https://pith.science/api/pith-number/K7ZE3SPFCCKTDLPZZDGCIDSUXH/events.json","paper":"https://pith.science/paper/K7ZE3SPF"},"agent_actions":{"view_html":"https://pith.science/pith/K7ZE3SPFCCKTDLPZZDGCIDSUXH","download_json":"https://pith.science/pith/K7ZE3SPFCCKTDLPZZDGCIDSUXH.json","view_paper":"https://pith.science/paper/K7ZE3SPF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.5168&json=true","fetch_graph":"https://pith.science/api/pith-number/K7ZE3SPFCCKTDLPZZDGCIDSUXH/graph.json","fetch_events":"https://pith.science/api/pith-number/K7ZE3SPFCCKTDLPZZDGCIDSUXH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K7ZE3SPFCCKTDLPZZDGCIDSUXH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K7ZE3SPFCCKTDLPZZDGCIDSUXH/action/storage_attestation","attest_author":"https://pith.science/pith/K7ZE3SPFCCKTDLPZZDGCIDSUXH/action/author_attestation","sign_citation":"https://pith.science/pith/K7ZE3SPFCCKTDLPZZDGCIDSUXH/action/citation_signature","submit_replication":"https://pith.science/pith/K7ZE3SPFCCKTDLPZZDGCIDSUXH/action/replication_record"}},"created_at":"2026-05-18T03:33:11.915907+00:00","updated_at":"2026-05-18T03:33:11.915907+00:00"}