{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CHTYNYHKTFAEPU7MUDK2KEJ2TN","short_pith_number":"pith:CHTYNYHK","canonical_record":{"source":{"id":"1109.2386","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-12T07:22:05Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"4bddac30a13771027b0b15c7a0a1cdd988b1b15a877cf9499fa68f3a2357b9a0","abstract_canon_sha256":"e4b55cbdee9664629356cb2ec3a0685a526aee7ee0575edb8fa2d616ef80722f"},"schema_version":"1.0"},"canonical_sha256":"11e786e0ea994047d3eca0d5a5113a9b6dc2ead46ec5faeb23770f74063cb5eb","source":{"kind":"arxiv","id":"1109.2386","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2386","created_at":"2026-05-18T03:50:23Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2386v3","created_at":"2026-05-18T03:50:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2386","created_at":"2026-05-18T03:50:23Z"},{"alias_kind":"pith_short_12","alias_value":"CHTYNYHKTFAE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CHTYNYHKTFAEPU7M","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CHTYNYHK","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CHTYNYHKTFAEPU7MUDK2KEJ2TN","target":"record","payload":{"canonical_record":{"source":{"id":"1109.2386","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-12T07:22:05Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"4bddac30a13771027b0b15c7a0a1cdd988b1b15a877cf9499fa68f3a2357b9a0","abstract_canon_sha256":"e4b55cbdee9664629356cb2ec3a0685a526aee7ee0575edb8fa2d616ef80722f"},"schema_version":"1.0"},"canonical_sha256":"11e786e0ea994047d3eca0d5a5113a9b6dc2ead46ec5faeb23770f74063cb5eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:23.032434Z","signature_b64":"sxGpuLNAogaEpXUDHJ/7oS+4s7CEfATo6DTSJk3LAz37Cv13qX255Dp8ttGbBSV+j/47cq/qfuTnEMoqzVCvAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11e786e0ea994047d3eca0d5a5113a9b6dc2ead46ec5faeb23770f74063cb5eb","last_reissued_at":"2026-05-18T03:50:23.031788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:23.031788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.2386","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:50:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XFom9sOgbicDy+MCmaxsE0NB5aFDeKR4ChhDpl3sJhGp0250SAmnSODH0hDoMmRbSswXV1zOfuoVovZ/LXQzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:47:15.790048Z"},"content_sha256":"7f6b302834a599f1c17f098ed5033b7260e075c4e33380f2a77b303d14500820","schema_version":"1.0","event_id":"sha256:7f6b302834a599f1c17f098ed5033b7260e075c4e33380f2a77b303d14500820"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CHTYNYHKTFAEPU7MUDK2KEJ2TN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate sampling formulae for general finite-alleles models of mutation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"math.PR","authors_text":"Anand Bhaskar, John A. Kamm, Yun S. Song","submitted_at":"2011-09-12T07:22:05Z","abstract_excerpt":"Many applications in genetic analyses utilize sampling distributions, which describe the probability of observing a sample of DNA sequences randomly drawn from a population. In the one-locus case with special models of mutation such as the infinite-alleles model or the finite-alleles parent-independent mutation model, closed-form sampling distributions under the coalescent have been known for many decades. However, no exact formula is currently known for more general models of mutation that are of biological interest. In this paper, models with finitely-many alleles are considered, and an urn "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2386","kind":"arxiv","version":3},"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":"2026-05-18T03:50:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ca24pOP+mGJbOMYMi7k2iwGk9vOrjk4trvvq8IVksETAoI0z/bkNWvTuU7Qd/kvjJgDM6FwP30bCVflYhCCEAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:47:15.790411Z"},"content_sha256":"ddb1a55ab1f988a034eccfe8c968bd7c2adc57afded53b23728783bd2cd0be07","schema_version":"1.0","event_id":"sha256:ddb1a55ab1f988a034eccfe8c968bd7c2adc57afded53b23728783bd2cd0be07"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CHTYNYHKTFAEPU7MUDK2KEJ2TN/bundle.json","state_url":"https://pith.science/pith/CHTYNYHKTFAEPU7MUDK2KEJ2TN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CHTYNYHKTFAEPU7MUDK2KEJ2TN/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":"2026-06-12T01:47:15Z","links":{"resolver":"https://pith.science/pith/CHTYNYHKTFAEPU7MUDK2KEJ2TN","bundle":"https://pith.science/pith/CHTYNYHKTFAEPU7MUDK2KEJ2TN/bundle.json","state":"https://pith.science/pith/CHTYNYHKTFAEPU7MUDK2KEJ2TN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CHTYNYHKTFAEPU7MUDK2KEJ2TN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CHTYNYHKTFAEPU7MUDK2KEJ2TN","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":"e4b55cbdee9664629356cb2ec3a0685a526aee7ee0575edb8fa2d616ef80722f","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-12T07:22:05Z","title_canon_sha256":"4bddac30a13771027b0b15c7a0a1cdd988b1b15a877cf9499fa68f3a2357b9a0"},"schema_version":"1.0","source":{"id":"1109.2386","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2386","created_at":"2026-05-18T03:50:23Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2386v3","created_at":"2026-05-18T03:50:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2386","created_at":"2026-05-18T03:50:23Z"},{"alias_kind":"pith_short_12","alias_value":"CHTYNYHKTFAE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CHTYNYHKTFAEPU7M","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CHTYNYHK","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:ddb1a55ab1f988a034eccfe8c968bd7c2adc57afded53b23728783bd2cd0be07","target":"graph","created_at":"2026-05-18T03:50:23Z","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":"Many applications in genetic analyses utilize sampling distributions, which describe the probability of observing a sample of DNA sequences randomly drawn from a population. In the one-locus case with special models of mutation such as the infinite-alleles model or the finite-alleles parent-independent mutation model, closed-form sampling distributions under the coalescent have been known for many decades. However, no exact formula is currently known for more general models of mutation that are of biological interest. In this paper, models with finitely-many alleles are considered, and an urn ","authors_text":"Anand Bhaskar, John A. Kamm, Yun S. Song","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-12T07:22:05Z","title":"Approximate sampling formulae for general finite-alleles models of mutation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2386","kind":"arxiv","version":3},"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":"sha256:7f6b302834a599f1c17f098ed5033b7260e075c4e33380f2a77b303d14500820","target":"record","created_at":"2026-05-18T03:50:23Z","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":"e4b55cbdee9664629356cb2ec3a0685a526aee7ee0575edb8fa2d616ef80722f","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-12T07:22:05Z","title_canon_sha256":"4bddac30a13771027b0b15c7a0a1cdd988b1b15a877cf9499fa68f3a2357b9a0"},"schema_version":"1.0","source":{"id":"1109.2386","kind":"arxiv","version":3}},"canonical_sha256":"11e786e0ea994047d3eca0d5a5113a9b6dc2ead46ec5faeb23770f74063cb5eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11e786e0ea994047d3eca0d5a5113a9b6dc2ead46ec5faeb23770f74063cb5eb","first_computed_at":"2026-05-18T03:50:23.031788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:23.031788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sxGpuLNAogaEpXUDHJ/7oS+4s7CEfATo6DTSJk3LAz37Cv13qX255Dp8ttGbBSV+j/47cq/qfuTnEMoqzVCvAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:23.032434Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2386","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f6b302834a599f1c17f098ed5033b7260e075c4e33380f2a77b303d14500820","sha256:ddb1a55ab1f988a034eccfe8c968bd7c2adc57afded53b23728783bd2cd0be07"],"state_sha256":"647bfb1bba2c107f53bb1504838928ce69e2c317a5f056fd1b3820d8faf465fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JBDMmzcAjdMt2bhMOeBWLX2uI/zm/eNRjK/dqO6B8UX9fxCXZqZNly2g/qGOT18ksnTQiCcQjwMCW6OmpOQ2CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T01:47:15.792390Z","bundle_sha256":"6a7be9fceb6ec423beafcc81f69b990612d168409d71ebaef7b72ec937603311"}}