{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NQWR3G3DER67WI2YMOX6JPROVC","short_pith_number":"pith:NQWR3G3D","canonical_record":{"source":{"id":"1704.08199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-26T16:37:39Z","cross_cats_sorted":[],"title_canon_sha256":"ea8503a5fb0456aa26dfa2c6074548ca8a9671c0e580fc31d699368f453eefd8","abstract_canon_sha256":"6195b1f40ec42d1f9ab44d2afeaf9f219517049ccb13b9792f79bdd2364ca620"},"schema_version":"1.0"},"canonical_sha256":"6c2d1d9b63247dfb235863afe4be2ea8bb6ccfeb13c3900cab83b4926baee713","source":{"kind":"arxiv","id":"1704.08199","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08199","created_at":"2026-05-18T00:45:30Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08199v1","created_at":"2026-05-18T00:45:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08199","created_at":"2026-05-18T00:45:30Z"},{"alias_kind":"pith_short_12","alias_value":"NQWR3G3DER67","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NQWR3G3DER67WI2Y","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NQWR3G3D","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NQWR3G3DER67WI2YMOX6JPROVC","target":"record","payload":{"canonical_record":{"source":{"id":"1704.08199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-26T16:37:39Z","cross_cats_sorted":[],"title_canon_sha256":"ea8503a5fb0456aa26dfa2c6074548ca8a9671c0e580fc31d699368f453eefd8","abstract_canon_sha256":"6195b1f40ec42d1f9ab44d2afeaf9f219517049ccb13b9792f79bdd2364ca620"},"schema_version":"1.0"},"canonical_sha256":"6c2d1d9b63247dfb235863afe4be2ea8bb6ccfeb13c3900cab83b4926baee713","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:30.940593Z","signature_b64":"YD1Nna4jIWUwc6fL9LTAalCp0hNqPGD0qIWfJ/TbGlXeGH7+XC4lZIVjUFq9DsEnwx+TQn+ZD4bi5Ib/g3e7DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c2d1d9b63247dfb235863afe4be2ea8bb6ccfeb13c3900cab83b4926baee713","last_reissued_at":"2026-05-18T00:45:30.940204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:30.940204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.08199","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":"2026-05-18T00:45:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cbosl1BKjdtmvtzDgB4Gie1y53U9woF0cfiEG11I3cJWusTBGzSD6zlXvPXLbfd07SNhuJpaLhuucz1gdRuaAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:13:26.193664Z"},"content_sha256":"a2b126dd5bea20a6fa68ebbcb0d755283d28e4c65ebd6d5a71420cef7452ead9","schema_version":"1.0","event_id":"sha256:a2b126dd5bea20a6fa68ebbcb0d755283d28e4c65ebd6d5a71420cef7452ead9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NQWR3G3DER67WI2YMOX6JPROVC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perpetual integrals convergence and extinctions in population dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Camille Coron, Denis Villemonais, Sylvie M\\'el\\'eard","submitted_at":"2017-04-26T16:37:39Z","abstract_excerpt":"In this article we use a criterion for the integrability of paths of one-dimensional diffusion processes from which we derive new insights on allelic fixation in several situations. This well known criterion involves a simple necessary and sufficient condition based on scale function and speed measure. We provide a new simple proof for this result and also obtain explicit bounds for the moments of such integrals. We also extend this criterion to non-homogeneous processes by use of Girsanov's transform. We apply our results to multi-type population dynamics: using the criterion with appropriate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08199","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":""},"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":"2026-05-18T00:45:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fvzl6oc6O/Ieq7qsibh03VUGVDgzH0R6pN7j3dywfvV6URGbiDA3tNQmpzP6veNyJ/6rGCBbqNStm90yJSuDAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:13:26.194048Z"},"content_sha256":"bbb5cba987737b035ce28afb32a1406c2a584aaa088379d6457bc3bc1e6a3eab","schema_version":"1.0","event_id":"sha256:bbb5cba987737b035ce28afb32a1406c2a584aaa088379d6457bc3bc1e6a3eab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NQWR3G3DER67WI2YMOX6JPROVC/bundle.json","state_url":"https://pith.science/pith/NQWR3G3DER67WI2YMOX6JPROVC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NQWR3G3DER67WI2YMOX6JPROVC/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":"2026-05-31T07:13:26Z","links":{"resolver":"https://pith.science/pith/NQWR3G3DER67WI2YMOX6JPROVC","bundle":"https://pith.science/pith/NQWR3G3DER67WI2YMOX6JPROVC/bundle.json","state":"https://pith.science/pith/NQWR3G3DER67WI2YMOX6JPROVC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NQWR3G3DER67WI2YMOX6JPROVC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NQWR3G3DER67WI2YMOX6JPROVC","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":"6195b1f40ec42d1f9ab44d2afeaf9f219517049ccb13b9792f79bdd2364ca620","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-26T16:37:39Z","title_canon_sha256":"ea8503a5fb0456aa26dfa2c6074548ca8a9671c0e580fc31d699368f453eefd8"},"schema_version":"1.0","source":{"id":"1704.08199","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08199","created_at":"2026-05-18T00:45:30Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08199v1","created_at":"2026-05-18T00:45:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08199","created_at":"2026-05-18T00:45:30Z"},{"alias_kind":"pith_short_12","alias_value":"NQWR3G3DER67","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NQWR3G3DER67WI2Y","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NQWR3G3D","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:bbb5cba987737b035ce28afb32a1406c2a584aaa088379d6457bc3bc1e6a3eab","target":"graph","created_at":"2026-05-18T00:45:30Z","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":"In this article we use a criterion for the integrability of paths of one-dimensional diffusion processes from which we derive new insights on allelic fixation in several situations. This well known criterion involves a simple necessary and sufficient condition based on scale function and speed measure. We provide a new simple proof for this result and also obtain explicit bounds for the moments of such integrals. We also extend this criterion to non-homogeneous processes by use of Girsanov's transform. We apply our results to multi-type population dynamics: using the criterion with appropriate","authors_text":"Camille Coron, Denis Villemonais, Sylvie M\\'el\\'eard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-26T16:37:39Z","title":"Perpetual integrals convergence and extinctions in population dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08199","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:a2b126dd5bea20a6fa68ebbcb0d755283d28e4c65ebd6d5a71420cef7452ead9","target":"record","created_at":"2026-05-18T00:45:30Z","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":"6195b1f40ec42d1f9ab44d2afeaf9f219517049ccb13b9792f79bdd2364ca620","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-26T16:37:39Z","title_canon_sha256":"ea8503a5fb0456aa26dfa2c6074548ca8a9671c0e580fc31d699368f453eefd8"},"schema_version":"1.0","source":{"id":"1704.08199","kind":"arxiv","version":1}},"canonical_sha256":"6c2d1d9b63247dfb235863afe4be2ea8bb6ccfeb13c3900cab83b4926baee713","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c2d1d9b63247dfb235863afe4be2ea8bb6ccfeb13c3900cab83b4926baee713","first_computed_at":"2026-05-18T00:45:30.940204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:30.940204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YD1Nna4jIWUwc6fL9LTAalCp0hNqPGD0qIWfJ/TbGlXeGH7+XC4lZIVjUFq9DsEnwx+TQn+ZD4bi5Ib/g3e7DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:30.940593Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.08199","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2b126dd5bea20a6fa68ebbcb0d755283d28e4c65ebd6d5a71420cef7452ead9","sha256:bbb5cba987737b035ce28afb32a1406c2a584aaa088379d6457bc3bc1e6a3eab"],"state_sha256":"8711dd339cf1d9fd323ae095d1463873e7ff21cd88636fefd34bb043a77f3e10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sOCT9aPq+tDg+/m2E50g9RKDFfmt4peSJ8NLq6LZpCv1Twynyo1+AtpnZ7b1Q+s3oK2D+lCAZ642rzLZ95GOAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T07:13:26.198540Z","bundle_sha256":"eac752c31a24d49e68b722c1e9893a0d1f897470bfa8e2a33c84a1cc83551a1d"}}