{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3PE6FK3PZHZCLK23KDB52IVG3N","short_pith_number":"pith:3PE6FK3P","canonical_record":{"source":{"id":"1506.01137","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2015-06-03T06:19:13Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"528615feb485f051c3fda8fa16f7fa35eeb2355e1c594fa9e3bdd429c93791ed","abstract_canon_sha256":"da42420cde16b0e5800ec32635b4c161a672dd943007598ea6a96233cf676e23"},"schema_version":"1.0"},"canonical_sha256":"dbc9e2ab6fc9f225ab5b50c3dd22a6db7d4c9ce04f732c0a907cb63c34519d0f","source":{"kind":"arxiv","id":"1506.01137","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01137","created_at":"2026-05-18T01:44:10Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01137v2","created_at":"2026-05-18T01:44:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01137","created_at":"2026-05-18T01:44:10Z"},{"alias_kind":"pith_short_12","alias_value":"3PE6FK3PZHZC","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3PE6FK3PZHZCLK23","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3PE6FK3P","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3PE6FK3PZHZCLK23KDB52IVG3N","target":"record","payload":{"canonical_record":{"source":{"id":"1506.01137","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2015-06-03T06:19:13Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"528615feb485f051c3fda8fa16f7fa35eeb2355e1c594fa9e3bdd429c93791ed","abstract_canon_sha256":"da42420cde16b0e5800ec32635b4c161a672dd943007598ea6a96233cf676e23"},"schema_version":"1.0"},"canonical_sha256":"dbc9e2ab6fc9f225ab5b50c3dd22a6db7d4c9ce04f732c0a907cb63c34519d0f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:10.871444Z","signature_b64":"XToCYHfl+qSRPnQK/grFaBO7mGim7Pce1LMPxHuMA4XDWPIJ8yMoGCU6Ms2LmiPyc718/wwMLieIBr1A0rNeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbc9e2ab6fc9f225ab5b50c3dd22a6db7d4c9ce04f732c0a907cb63c34519d0f","last_reissued_at":"2026-05-18T01:44:10.870807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:10.870807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.01137","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":"2026-05-18T01:44:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HeKr0EAzSjyaMWFAWJH1glXNS/58g5uJzCNZ1xNsoRSoEf7eXJObZLM/EnELpm9S2rqPadUO/LF1kj7zykQ1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:57:18.917755Z"},"content_sha256":"04ecea50a71c013859bba43f7213064ece6feab64032a8e8225d0987862b0765","schema_version":"1.0","event_id":"sha256:04ecea50a71c013859bba43f7213064ece6feab64032a8e8225d0987862b0765"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3PE6FK3PZHZCLK23KDB52IVG3N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic dynamics and logistic population growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"q-bio.PE","authors_text":"Daniel Campos, Michael Assaf, Vicen\\c{c} M\\'endez, Werner Horsthemke","submitted_at":"2015-06-03T06:19:13Z","abstract_excerpt":"The Verhulst model is probably the best known macroscopic rate equation in population ecology. It depends on two parameters, the intrinsic growth rate and the carrying capacity. These parameters can be estimated for different populations and are related to the reproductive fitness and the competition for limited resources, respectively. We investigate analytically and numerically the simplest possible microscopic scenarios that give rise to the logistic equation in the deterministic mean-field limit. We provide a definition of the two parameters of the Verhulst equation in terms of microscopic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01137","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":"2026-05-18T01:44:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ysny3S+hAjbita4hTuu0FZufKmG80YsgZP4OqEg14Xg5iYd3FpNHhnrDlBU5ugnhiQN1GJ/wREH3L4gdxN1lAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:57:18.918434Z"},"content_sha256":"e726c87a5c835f71f39eb80bf72430bf37d456bf1d6414fab8cedd9d43e50d70","schema_version":"1.0","event_id":"sha256:e726c87a5c835f71f39eb80bf72430bf37d456bf1d6414fab8cedd9d43e50d70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3PE6FK3PZHZCLK23KDB52IVG3N/bundle.json","state_url":"https://pith.science/pith/3PE6FK3PZHZCLK23KDB52IVG3N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3PE6FK3PZHZCLK23KDB52IVG3N/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":"2026-05-27T17:57:18Z","links":{"resolver":"https://pith.science/pith/3PE6FK3PZHZCLK23KDB52IVG3N","bundle":"https://pith.science/pith/3PE6FK3PZHZCLK23KDB52IVG3N/bundle.json","state":"https://pith.science/pith/3PE6FK3PZHZCLK23KDB52IVG3N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3PE6FK3PZHZCLK23KDB52IVG3N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3PE6FK3PZHZCLK23KDB52IVG3N","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":"da42420cde16b0e5800ec32635b4c161a672dd943007598ea6a96233cf676e23","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2015-06-03T06:19:13Z","title_canon_sha256":"528615feb485f051c3fda8fa16f7fa35eeb2355e1c594fa9e3bdd429c93791ed"},"schema_version":"1.0","source":{"id":"1506.01137","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01137","created_at":"2026-05-18T01:44:10Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01137v2","created_at":"2026-05-18T01:44:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01137","created_at":"2026-05-18T01:44:10Z"},{"alias_kind":"pith_short_12","alias_value":"3PE6FK3PZHZC","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3PE6FK3PZHZCLK23","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3PE6FK3P","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:e726c87a5c835f71f39eb80bf72430bf37d456bf1d6414fab8cedd9d43e50d70","target":"graph","created_at":"2026-05-18T01:44:10Z","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":"The Verhulst model is probably the best known macroscopic rate equation in population ecology. It depends on two parameters, the intrinsic growth rate and the carrying capacity. These parameters can be estimated for different populations and are related to the reproductive fitness and the competition for limited resources, respectively. We investigate analytically and numerically the simplest possible microscopic scenarios that give rise to the logistic equation in the deterministic mean-field limit. We provide a definition of the two parameters of the Verhulst equation in terms of microscopic","authors_text":"Daniel Campos, Michael Assaf, Vicen\\c{c} M\\'endez, Werner Horsthemke","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2015-06-03T06:19:13Z","title":"Stochastic dynamics and logistic population growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01137","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":"sha256:04ecea50a71c013859bba43f7213064ece6feab64032a8e8225d0987862b0765","target":"record","created_at":"2026-05-18T01:44:10Z","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":"da42420cde16b0e5800ec32635b4c161a672dd943007598ea6a96233cf676e23","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2015-06-03T06:19:13Z","title_canon_sha256":"528615feb485f051c3fda8fa16f7fa35eeb2355e1c594fa9e3bdd429c93791ed"},"schema_version":"1.0","source":{"id":"1506.01137","kind":"arxiv","version":2}},"canonical_sha256":"dbc9e2ab6fc9f225ab5b50c3dd22a6db7d4c9ce04f732c0a907cb63c34519d0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbc9e2ab6fc9f225ab5b50c3dd22a6db7d4c9ce04f732c0a907cb63c34519d0f","first_computed_at":"2026-05-18T01:44:10.870807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:44:10.870807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XToCYHfl+qSRPnQK/grFaBO7mGim7Pce1LMPxHuMA4XDWPIJ8yMoGCU6Ms2LmiPyc718/wwMLieIBr1A0rNeBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:44:10.871444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01137","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04ecea50a71c013859bba43f7213064ece6feab64032a8e8225d0987862b0765","sha256:e726c87a5c835f71f39eb80bf72430bf37d456bf1d6414fab8cedd9d43e50d70"],"state_sha256":"58427ad847d081ce6e1cedcf9c83a4a6b99fe17dd2d91d1da7f674010b0c99a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dw/fMqFOcaSJ5XxbaxTOCq/ETz76DN0JasECHLfGOSUx85t2G/O/WjvvPgauvtWiDEMMREGA4RG8C7/iUR5mAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T17:57:18.921701Z","bundle_sha256":"075c956d0912713df5e9ed297887b2a76088a2fe775c7f258f0e0fad093076c0"}}