{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:EMY5VYMRJDOFJC4C5MP3XVG3U4","short_pith_number":"pith:EMY5VYMR","canonical_record":{"source":{"id":"2507.19659","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.PE","submitted_at":"2025-07-25T20:09:20Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"cb4c05944503247351ec3e15d5d3666335ffffc8e7bf48d49e548e33e3ea232e","abstract_canon_sha256":"aafe8bdb78b670968aac7a3939237f2303a872e88458158f3fc975fc18f50426"},"schema_version":"1.0"},"canonical_sha256":"2331dae19148dc548b82eb1fbbd4dba724519189f2f1bcbb75ad9965ed8d3a96","source":{"kind":"arxiv","id":"2507.19659","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.19659","created_at":"2026-07-05T11:43:38Z"},{"alias_kind":"arxiv_version","alias_value":"2507.19659v1","created_at":"2026-07-05T11:43:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.19659","created_at":"2026-07-05T11:43:38Z"},{"alias_kind":"pith_short_12","alias_value":"EMY5VYMRJDOF","created_at":"2026-07-05T11:43:38Z"},{"alias_kind":"pith_short_16","alias_value":"EMY5VYMRJDOFJC4C","created_at":"2026-07-05T11:43:38Z"},{"alias_kind":"pith_short_8","alias_value":"EMY5VYMR","created_at":"2026-07-05T11:43:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:EMY5VYMRJDOFJC4C5MP3XVG3U4","target":"record","payload":{"canonical_record":{"source":{"id":"2507.19659","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.PE","submitted_at":"2025-07-25T20:09:20Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"cb4c05944503247351ec3e15d5d3666335ffffc8e7bf48d49e548e33e3ea232e","abstract_canon_sha256":"aafe8bdb78b670968aac7a3939237f2303a872e88458158f3fc975fc18f50426"},"schema_version":"1.0"},"canonical_sha256":"2331dae19148dc548b82eb1fbbd4dba724519189f2f1bcbb75ad9965ed8d3a96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:43:38.683934Z","signature_b64":"CtTaJ7jNkTAxDHIMrxzQGHHLyI+ec+Xb5sJzigbk5JOXpgCa4SG4qaGGuF68uWNW8V86c6aMd76QAtrhi7LyCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2331dae19148dc548b82eb1fbbd4dba724519189f2f1bcbb75ad9965ed8d3a96","last_reissued_at":"2026-07-05T11:43:38.683339Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:43:38.683339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.19659","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:43:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IfXMxaKbBqB50NQMQ0B3W6SHUQ+6rHpaoaKA+UaB+A5z8abQrFjOIdgETYMa6PrUtLQfOQGYEDMW+7BA9l6SDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T05:32:39.962124Z"},"content_sha256":"df464896c5dd3ce9f2d4f8a399b0efc5b661e1faf565e4968c5542e2b38b6b1d","schema_version":"1.0","event_id":"sha256:df464896c5dd3ce9f2d4f8a399b0efc5b661e1faf565e4968c5542e2b38b6b1d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:EMY5VYMRJDOFJC4C5MP3XVG3U4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Posterior bounds on divergence time of two sequences under dependent-site evolutionary models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-bio.PE","authors_text":"Joseph Mathews, Scott C. Schmidler","submitted_at":"2025-07-25T20:09:20Z","abstract_excerpt":"Let x and y be two length n DNA sequences, and suppose we would like to estimate the divergence time T. A well known simple but crude estimate of T is p := d(x,y)/n, the fraction of mutated sites (the p-distance). We establish a posterior concentration bound on T, showing that the posterior distribution of T concentrates within a logarithmic factor of p when d(x,y)log(n)/n = o(1). Our bounds hold under a large class of evolutionary models, including many standard models that incorporate site dependence. As a special case, we show that T exceeds p with vanishingly small posterior probability as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19659","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.19659/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:43:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BieskY/WjTBBXxUNGbJ4PqSEjaUXGKN3pnLj0fd1UYBf9pqh3VZOHQaxjGiuFafRsShw+1iDEUTjDsiZVNQWCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T05:32:39.962621Z"},"content_sha256":"0ca451caa9499df8914656a33fd5bc85183bb31f8b8a73cd14179ba11cdf821a","schema_version":"1.0","event_id":"sha256:0ca451caa9499df8914656a33fd5bc85183bb31f8b8a73cd14179ba11cdf821a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EMY5VYMRJDOFJC4C5MP3XVG3U4/bundle.json","state_url":"https://pith.science/pith/EMY5VYMRJDOFJC4C5MP3XVG3U4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EMY5VYMRJDOFJC4C5MP3XVG3U4/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":"2026-08-22T05:32:39Z","links":{"resolver":"https://pith.science/pith/EMY5VYMRJDOFJC4C5MP3XVG3U4","bundle":"https://pith.science/pith/EMY5VYMRJDOFJC4C5MP3XVG3U4/bundle.json","state":"https://pith.science/pith/EMY5VYMRJDOFJC4C5MP3XVG3U4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EMY5VYMRJDOFJC4C5MP3XVG3U4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EMY5VYMRJDOFJC4C5MP3XVG3U4","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":"aafe8bdb78b670968aac7a3939237f2303a872e88458158f3fc975fc18f50426","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.PE","submitted_at":"2025-07-25T20:09:20Z","title_canon_sha256":"cb4c05944503247351ec3e15d5d3666335ffffc8e7bf48d49e548e33e3ea232e"},"schema_version":"1.0","source":{"id":"2507.19659","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.19659","created_at":"2026-07-05T11:43:38Z"},{"alias_kind":"arxiv_version","alias_value":"2507.19659v1","created_at":"2026-07-05T11:43:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.19659","created_at":"2026-07-05T11:43:38Z"},{"alias_kind":"pith_short_12","alias_value":"EMY5VYMRJDOF","created_at":"2026-07-05T11:43:38Z"},{"alias_kind":"pith_short_16","alias_value":"EMY5VYMRJDOFJC4C","created_at":"2026-07-05T11:43:38Z"},{"alias_kind":"pith_short_8","alias_value":"EMY5VYMR","created_at":"2026-07-05T11:43:38Z"}],"graph_snapshots":[{"event_id":"sha256:0ca451caa9499df8914656a33fd5bc85183bb31f8b8a73cd14179ba11cdf821a","target":"graph","created_at":"2026-07-05T11:43:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.19659/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let x and y be two length n DNA sequences, and suppose we would like to estimate the divergence time T. A well known simple but crude estimate of T is p := d(x,y)/n, the fraction of mutated sites (the p-distance). We establish a posterior concentration bound on T, showing that the posterior distribution of T concentrates within a logarithmic factor of p when d(x,y)log(n)/n = o(1). Our bounds hold under a large class of evolutionary models, including many standard models that incorporate site dependence. As a special case, we show that T exceeds p with vanishingly small posterior probability as","authors_text":"Joseph Mathews, Scott C. Schmidler","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.PE","submitted_at":"2025-07-25T20:09:20Z","title":"Posterior bounds on divergence time of two sequences under dependent-site evolutionary models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19659","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:df464896c5dd3ce9f2d4f8a399b0efc5b661e1faf565e4968c5542e2b38b6b1d","target":"record","created_at":"2026-07-05T11:43:38Z","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":"aafe8bdb78b670968aac7a3939237f2303a872e88458158f3fc975fc18f50426","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.PE","submitted_at":"2025-07-25T20:09:20Z","title_canon_sha256":"cb4c05944503247351ec3e15d5d3666335ffffc8e7bf48d49e548e33e3ea232e"},"schema_version":"1.0","source":{"id":"2507.19659","kind":"arxiv","version":1}},"canonical_sha256":"2331dae19148dc548b82eb1fbbd4dba724519189f2f1bcbb75ad9965ed8d3a96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2331dae19148dc548b82eb1fbbd4dba724519189f2f1bcbb75ad9965ed8d3a96","first_computed_at":"2026-07-05T11:43:38.683339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:43:38.683339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CtTaJ7jNkTAxDHIMrxzQGHHLyI+ec+Xb5sJzigbk5JOXpgCa4SG4qaGGuF68uWNW8V86c6aMd76QAtrhi7LyCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:43:38.683934Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.19659","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df464896c5dd3ce9f2d4f8a399b0efc5b661e1faf565e4968c5542e2b38b6b1d","sha256:0ca451caa9499df8914656a33fd5bc85183bb31f8b8a73cd14179ba11cdf821a"],"state_sha256":"0337469b793999d2c17fa249a1e0d54acaf66d14f2d483fdb3671f293fe39190"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3dZdUHXXSaqo/ukG+ai2Gf3FfTfEhZ+F06Y6JXJG4mLkgdVQOzXpNDtRolGOufZ4dTA71YKXHrkYLw+hEU48AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T05:32:39.967207Z","bundle_sha256":"7acf2950458ecb4ab0ce885b600c4c53e5f08d6fa2651332ea2c719952d7ee73"}}