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The phylogeny graph $P(D)$ of a digraph $D$ is the (simple undirected) graph defined by $V(P(D)):=V(D)$ and $E(P(D)):=\\{xy \\mid N^+_D(x) \\cap N^+_D(y) \\neq \\emptyset \\} \\cup \\{xy \\mid (x,y) \\in A(D) \\}$, where $N^+_D(x):=\\{v \\in V(D) \\mid (x,v) \\in A(D)\\}$.\n  In this n"},"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":"1103.4540","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-03-23T14:46:28Z","cross_cats_sorted":[],"title_canon_sha256":"448c6b2b2ffcc8f34c7e31a8a047ceafd19077750edea5f9fa7a5dd89a12f01b","abstract_canon_sha256":"d39b315ebc76b373ef71d12004ec4df2d6cd4726de463c7a4d1440c07022b707"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:23.260447Z","signature_b64":"e38OYZQ14jAibUOfQ7CQTKqLKgqb9Zt8K4fHLUPbAz0Qs+KfSAAxMpIXvsrt0Fz8pQQIU2p0hVY81CyxX0E6Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b39d4c4abb4f0899af6f487164aa019124b443d9720a3904d3c6b90f43b1c2f","last_reissued_at":"2026-05-18T03:09:23.259520Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:23.259520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The phylogeny graphs of doubly partial orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Boram Park, Yoshio Sano","submitted_at":"2011-03-23T14:46:28Z","abstract_excerpt":"The competition graph of a doubly partial order is known to be an interval graph. 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