{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:X6XYC4WVPWUPIVI54XTDWRMMSO","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":"258c32a1886b21022c8e622f452bfbb022773c3b45c0d35b8ce5a8a88fdba8c9","cross_cats_sorted":["physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2014-07-29T18:49:36Z","title_canon_sha256":"5fafcd0ae46b3bf04a5ea68bda251c140f9e20a629c5d4b0cd4d10c1f3ba339a"},"schema_version":"1.0","source":{"id":"1407.7821","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7821","created_at":"2026-05-18T02:19:50Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7821v2","created_at":"2026-05-18T02:19:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7821","created_at":"2026-05-18T02:19:50Z"},{"alias_kind":"pith_short_12","alias_value":"X6XYC4WVPWUP","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"X6XYC4WVPWUPIVI5","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"X6XYC4WV","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:d55e756675e8ee35597fa595474bda3e024717d14a5654bdef5a4f5a1a0fe344","target":"graph","created_at":"2026-05-18T02:19:50Z","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":"A Yule tree is the result of a branching process with constant birth and death rates. Such a process serves as an instructive null model of many empirical systems, for instance, the evolution of species leading to a phylogenetic tree. However, often in phylogeny the only available information is the pairwise distances between a small fraction of extant species representing the leaves of the tree. In this article we study statistical properties of the pairwise distances in a Yule tree. Using a method based on a recursion, we derive an exact, analytic and compact formula for the expected number ","authors_text":"Florian Massip, Michael Sheinman, Peter F. Arndt","cross_cats":["physics.bio-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2014-07-29T18:49:36Z","title":"Statistical Properties of Pairwise Distances between Leaves on a Random Yule Tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7821","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:ea2c3d2f6d0f2d1975a4a510b1f9df1f527f3d9beda0ebdc875c2f4efa0cfdce","target":"record","created_at":"2026-05-18T02:19:50Z","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":"258c32a1886b21022c8e622f452bfbb022773c3b45c0d35b8ce5a8a88fdba8c9","cross_cats_sorted":["physics.bio-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2014-07-29T18:49:36Z","title_canon_sha256":"5fafcd0ae46b3bf04a5ea68bda251c140f9e20a629c5d4b0cd4d10c1f3ba339a"},"schema_version":"1.0","source":{"id":"1407.7821","kind":"arxiv","version":2}},"canonical_sha256":"bfaf8172d57da8f4551de5e63b458c9399aad1bfd1832cde43b6a0a9d14db4b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfaf8172d57da8f4551de5e63b458c9399aad1bfd1832cde43b6a0a9d14db4b8","first_computed_at":"2026-05-18T02:19:50.476993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:50.476993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NteNOFpsCoJV6xBz+3Ctr77JegDc9PyCFFH9KvidJ1wkO1oPiD25+skaHmU2LpHvtIrTZGs2ZG0/zUkR/DpdBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:50.477717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.7821","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea2c3d2f6d0f2d1975a4a510b1f9df1f527f3d9beda0ebdc875c2f4efa0cfdce","sha256:d55e756675e8ee35597fa595474bda3e024717d14a5654bdef5a4f5a1a0fe344"],"state_sha256":"cd8b24d87ec61d17dd6ef5293dd93c540322fc265635c40616e18a26a76cfe7d"}