{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:UAYC5EAHCLFOXULY5MMUU5WGMA","short_pith_number":"pith:UAYC5EAH","canonical_record":{"source":{"id":"2306.03539","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-06-06T09:37:17Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"6865893cf3d05b9b84df6f988d9f4cbe77fc606b025fca10a36f42972dd69aba","abstract_canon_sha256":"b9fb37c28bda8efe96908215b6f8162555c60aae70926d7623b3f581a042317f"},"schema_version":"1.0"},"canonical_sha256":"a0302e900712caebd178eb194a76c660341edbdbcc2db391f7f987f7a6c8f438","source":{"kind":"arxiv","id":"2306.03539","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.03539","created_at":"2026-07-05T07:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"2306.03539v3","created_at":"2026-07-05T07:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.03539","created_at":"2026-07-05T07:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"UAYC5EAHCLFO","created_at":"2026-07-05T07:39:59Z"},{"alias_kind":"pith_short_16","alias_value":"UAYC5EAHCLFOXULY","created_at":"2026-07-05T07:39:59Z"},{"alias_kind":"pith_short_8","alias_value":"UAYC5EAH","created_at":"2026-07-05T07:39:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:UAYC5EAHCLFOXULY5MMUU5WGMA","target":"record","payload":{"canonical_record":{"source":{"id":"2306.03539","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-06-06T09:37:17Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"6865893cf3d05b9b84df6f988d9f4cbe77fc606b025fca10a36f42972dd69aba","abstract_canon_sha256":"b9fb37c28bda8efe96908215b6f8162555c60aae70926d7623b3f581a042317f"},"schema_version":"1.0"},"canonical_sha256":"a0302e900712caebd178eb194a76c660341edbdbcc2db391f7f987f7a6c8f438","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:39:59.213630Z","signature_b64":"h3tEwMmydHD9IwMX8xkmiwwkr37AKWNUwmXaAJ1Bz2YhtLRXy0GPOpk/Il8fXQCAIqSyECd8s2l55gnukklmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0302e900712caebd178eb194a76c660341edbdbcc2db391f7f987f7a6c8f438","last_reissued_at":"2026-07-05T07:39:59.213215Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:39:59.213215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.03539","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":"2026-07-05T07:39:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+cDKZDGFlK405YkCHdczbehoNVPYE1YnjJcUqUPQ6Z3jpY06o0Z2H9PuZrhIIKwvAiKVNPne1fuKbxUpoXbFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T06:14:17.012601Z"},"content_sha256":"78b6e8eef948a8f0e580832d8d43a9c6a590d5c5bcdda281c9c1d717d63e8f75","schema_version":"1.0","event_id":"sha256:78b6e8eef948a8f0e580832d8d43a9c6a590d5c5bcdda281c9c1d717d63e8f75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:UAYC5EAHCLFOXULY5MMUU5WGMA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bernoulli factories and duality in Wright-Fisher and Allen-Cahn models of population genetics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"math.PR","authors_text":"Dario Span\\`o, Jere Koskela, Krzysztof {\\L}atuszy\\'nski","submitted_at":"2023-06-06T09:37:17Z","abstract_excerpt":"Mathematical models of genetic evolution often come in pairs, connected by a so-called duality relation. The most seminal example are the Wright-Fisher diffusion and the Kingman coalescent, where the former describes the stochastic evolution of neutral allele frequencies in a large population forwards in time, and the latter describes the genetic ancestry of randomly sampled individuals from the population backwards in time. As well as providing a richer description than either model in isolation, duality often yields equations satisfied by quantities of interest. We employ the so-called Berno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.03539","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.03539/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":"2026-07-05T07:39:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ju4e+1634Fc3psCmcliUszZeZmpmMkOswnVcMe1imnnaHdG1ujkhS4nKjZXkDYplGOq+nnNqLPneH0hzuTnRDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T06:14:17.013140Z"},"content_sha256":"1395914af73191d9089dd3db29a1edc88bd27efd1aa7c2ddc0f95f39ee9a51ca","schema_version":"1.0","event_id":"sha256:1395914af73191d9089dd3db29a1edc88bd27efd1aa7c2ddc0f95f39ee9a51ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UAYC5EAHCLFOXULY5MMUU5WGMA/bundle.json","state_url":"https://pith.science/pith/UAYC5EAHCLFOXULY5MMUU5WGMA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UAYC5EAHCLFOXULY5MMUU5WGMA/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":"2026-08-15T06:14:17Z","links":{"resolver":"https://pith.science/pith/UAYC5EAHCLFOXULY5MMUU5WGMA","bundle":"https://pith.science/pith/UAYC5EAHCLFOXULY5MMUU5WGMA/bundle.json","state":"https://pith.science/pith/UAYC5EAHCLFOXULY5MMUU5WGMA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UAYC5EAHCLFOXULY5MMUU5WGMA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:UAYC5EAHCLFOXULY5MMUU5WGMA","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":"b9fb37c28bda8efe96908215b6f8162555c60aae70926d7623b3f581a042317f","cross_cats_sorted":["q-bio.PE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-06-06T09:37:17Z","title_canon_sha256":"6865893cf3d05b9b84df6f988d9f4cbe77fc606b025fca10a36f42972dd69aba"},"schema_version":"1.0","source":{"id":"2306.03539","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.03539","created_at":"2026-07-05T07:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"2306.03539v3","created_at":"2026-07-05T07:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.03539","created_at":"2026-07-05T07:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"UAYC5EAHCLFO","created_at":"2026-07-05T07:39:59Z"},{"alias_kind":"pith_short_16","alias_value":"UAYC5EAHCLFOXULY","created_at":"2026-07-05T07:39:59Z"},{"alias_kind":"pith_short_8","alias_value":"UAYC5EAH","created_at":"2026-07-05T07:39:59Z"}],"graph_snapshots":[{"event_id":"sha256:1395914af73191d9089dd3db29a1edc88bd27efd1aa7c2ddc0f95f39ee9a51ca","target":"graph","created_at":"2026-07-05T07:39:59Z","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/2306.03539/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Mathematical models of genetic evolution often come in pairs, connected by a so-called duality relation. The most seminal example are the Wright-Fisher diffusion and the Kingman coalescent, where the former describes the stochastic evolution of neutral allele frequencies in a large population forwards in time, and the latter describes the genetic ancestry of randomly sampled individuals from the population backwards in time. As well as providing a richer description than either model in isolation, duality often yields equations satisfied by quantities of interest. We employ the so-called Berno","authors_text":"Dario Span\\`o, Jere Koskela, Krzysztof {\\L}atuszy\\'nski","cross_cats":["q-bio.PE"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-06-06T09:37:17Z","title":"Bernoulli factories and duality in Wright-Fisher and Allen-Cahn models of population genetics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.03539","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":"sha256:78b6e8eef948a8f0e580832d8d43a9c6a590d5c5bcdda281c9c1d717d63e8f75","target":"record","created_at":"2026-07-05T07:39:59Z","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":"b9fb37c28bda8efe96908215b6f8162555c60aae70926d7623b3f581a042317f","cross_cats_sorted":["q-bio.PE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-06-06T09:37:17Z","title_canon_sha256":"6865893cf3d05b9b84df6f988d9f4cbe77fc606b025fca10a36f42972dd69aba"},"schema_version":"1.0","source":{"id":"2306.03539","kind":"arxiv","version":3}},"canonical_sha256":"a0302e900712caebd178eb194a76c660341edbdbcc2db391f7f987f7a6c8f438","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0302e900712caebd178eb194a76c660341edbdbcc2db391f7f987f7a6c8f438","first_computed_at":"2026-07-05T07:39:59.213215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:39:59.213215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h3tEwMmydHD9IwMX8xkmiwwkr37AKWNUwmXaAJ1Bz2YhtLRXy0GPOpk/Il8fXQCAIqSyECd8s2l55gnukklmBA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:39:59.213630Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.03539","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78b6e8eef948a8f0e580832d8d43a9c6a590d5c5bcdda281c9c1d717d63e8f75","sha256:1395914af73191d9089dd3db29a1edc88bd27efd1aa7c2ddc0f95f39ee9a51ca"],"state_sha256":"507332e031286ca7e15ed09be6fda191257e8a4991f5e1332e2caa2e2e25db5e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y6fV1JTqIXddMNbtlsg6jg4x9BmtmJpjMPA1uLP05P03UNE6iJd8rl4TqTGRzjIofYEpTee2Eh1gUTX4nwh9DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T06:14:17.016188Z","bundle_sha256":"3cf5999fd3731189361166188cf5e785f51613f023dd83ae11dfe9fa62215d37"}}