{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:X6XYC4WVPWUPIVI54XTDWRMMSO","short_pith_number":"pith:X6XYC4WV","canonical_record":{"source":{"id":"1407.7821","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2014-07-29T18:49:36Z","cross_cats_sorted":["physics.bio-ph"],"title_canon_sha256":"5fafcd0ae46b3bf04a5ea68bda251c140f9e20a629c5d4b0cd4d10c1f3ba339a","abstract_canon_sha256":"258c32a1886b21022c8e622f452bfbb022773c3b45c0d35b8ce5a8a88fdba8c9"},"schema_version":"1.0"},"canonical_sha256":"bfaf8172d57da8f4551de5e63b458c9399aad1bfd1832cde43b6a0a9d14db4b8","source":{"kind":"arxiv","id":"1407.7821","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:X6XYC4WVPWUPIVI54XTDWRMMSO","target":"record","payload":{"canonical_record":{"source":{"id":"1407.7821","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2014-07-29T18:49:36Z","cross_cats_sorted":["physics.bio-ph"],"title_canon_sha256":"5fafcd0ae46b3bf04a5ea68bda251c140f9e20a629c5d4b0cd4d10c1f3ba339a","abstract_canon_sha256":"258c32a1886b21022c8e622f452bfbb022773c3b45c0d35b8ce5a8a88fdba8c9"},"schema_version":"1.0"},"canonical_sha256":"bfaf8172d57da8f4551de5e63b458c9399aad1bfd1832cde43b6a0a9d14db4b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:50.477717Z","signature_b64":"NteNOFpsCoJV6xBz+3Ctr77JegDc9PyCFFH9KvidJ1wkO1oPiD25+skaHmU2LpHvtIrTZGs2ZG0/zUkR/DpdBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfaf8172d57da8f4551de5e63b458c9399aad1bfd1832cde43b6a0a9d14db4b8","last_reissued_at":"2026-05-18T02:19:50.476993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:50.476993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.7821","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:19:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fmpP78MOSxBX/WwjALAhMsMhVqJIAU4Ra+a1VKiR4Es1cFl1sbAz8nNivPGPhG92GlWwC7U8/XmbKkyS1dKbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T11:34:37.920664Z"},"content_sha256":"ea2c3d2f6d0f2d1975a4a510b1f9df1f527f3d9beda0ebdc875c2f4efa0cfdce","schema_version":"1.0","event_id":"sha256:ea2c3d2f6d0f2d1975a4a510b1f9df1f527f3d9beda0ebdc875c2f4efa0cfdce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:X6XYC4WVPWUPIVI54XTDWRMMSO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical Properties of Pairwise Distances between Leaves on a Random Yule Tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.bio-ph"],"primary_cat":"q-bio.PE","authors_text":"Florian Massip, Michael Sheinman, Peter F. Arndt","submitted_at":"2014-07-29T18:49:36Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7821","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:19:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q5/FjOdQYMjw7vwNcx4FBzEA19PzRKi7RhTDV5aJbyTihBlzlUvpCU35T3K4xJZH6vCmbUhREstyE3QOxRPGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T11:34:37.921390Z"},"content_sha256":"d55e756675e8ee35597fa595474bda3e024717d14a5654bdef5a4f5a1a0fe344","schema_version":"1.0","event_id":"sha256:d55e756675e8ee35597fa595474bda3e024717d14a5654bdef5a4f5a1a0fe344"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X6XYC4WVPWUPIVI54XTDWRMMSO/bundle.json","state_url":"https://pith.science/pith/X6XYC4WVPWUPIVI54XTDWRMMSO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X6XYC4WVPWUPIVI54XTDWRMMSO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-23T11:34:37Z","links":{"resolver":"https://pith.science/pith/X6XYC4WVPWUPIVI54XTDWRMMSO","bundle":"https://pith.science/pith/X6XYC4WVPWUPIVI54XTDWRMMSO/bundle.json","state":"https://pith.science/pith/X6XYC4WVPWUPIVI54XTDWRMMSO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X6XYC4WVPWUPIVI54XTDWRMMSO/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mgESiwxG6Zu393V14wPrXgTSdmgCSNt8hVEN6LSGKRcoK/iAd0KQTS9BkH/4ZcbAoax9oI5Xc8ov5ifShyj6Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T11:34:37.925461Z","bundle_sha256":"5a41175b1576ced4a861dcd84aa03b3246875b5114a067efc73ee35f273f334b"}}