{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UAILLCAVVXFKF7HHYSZEZ4OD5P","short_pith_number":"pith:UAILLCAV","canonical_record":{"source":{"id":"1205.1367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2012-05-07T12:56:10Z","cross_cats_sorted":["physics.bio-ph","physics.soc-ph"],"title_canon_sha256":"c4199b1aca7cd681257f60c43015feab06984d1cde70b3140edd59c262b331ed","abstract_canon_sha256":"97b92840217289824f914395a3988487d99b03def5e244039ae1ce2b209ddeee"},"schema_version":"1.0"},"canonical_sha256":"a010b58815adcaa2fce7c4b24cf1c3ebd98a7d43d7184ef2a5debc97876cf4bb","source":{"kind":"arxiv","id":"1205.1367","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1367","created_at":"2026-05-18T01:57:37Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1367v1","created_at":"2026-05-18T01:57:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1367","created_at":"2026-05-18T01:57:37Z"},{"alias_kind":"pith_short_12","alias_value":"UAILLCAVVXFK","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UAILLCAVVXFKF7HH","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UAILLCAV","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UAILLCAVVXFKF7HHYSZEZ4OD5P","target":"record","payload":{"canonical_record":{"source":{"id":"1205.1367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2012-05-07T12:56:10Z","cross_cats_sorted":["physics.bio-ph","physics.soc-ph"],"title_canon_sha256":"c4199b1aca7cd681257f60c43015feab06984d1cde70b3140edd59c262b331ed","abstract_canon_sha256":"97b92840217289824f914395a3988487d99b03def5e244039ae1ce2b209ddeee"},"schema_version":"1.0"},"canonical_sha256":"a010b58815adcaa2fce7c4b24cf1c3ebd98a7d43d7184ef2a5debc97876cf4bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:37.343829Z","signature_b64":"icHsYsPf3riNW9tq5ISkAdd37fAIZmmasyBQTpTR2JEat/VF2v2gl+cpboMV+ygf0abWOWX9IHEk/DDyhkNQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a010b58815adcaa2fce7c4b24cf1c3ebd98a7d43d7184ef2a5debc97876cf4bb","last_reissued_at":"2026-05-18T01:57:37.343087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:37.343087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.1367","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":"2026-05-18T01:57:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4F6rw9Hs/iQW4xpHRI7JUHQm4QnRdRvD5dvbTnqZJEQKTGt0oNnEZBRqqTp+KQdMjsljHeLPdUEKQZRIT0mDAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:36:33.868093Z"},"content_sha256":"48847f7db3affe0ed99f590db913041dac083df0be3b80a0708c60d0c3a5996a","schema_version":"1.0","event_id":"sha256:48847f7db3affe0ed99f590db913041dac083df0be3b80a0708c60d0c3a5996a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UAILLCAVVXFKF7HHYSZEZ4OD5P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extreme events in population dynamics with functional carrying capacity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.bio-ph","physics.soc-ph"],"primary_cat":"q-bio.PE","authors_text":"D. Sornette, E. P. Yukalova, V. I. Yukalov","submitted_at":"2012-05-07T12:56:10Z","abstract_excerpt":"A class of models is introduced describing the evolution of population species whose carrying capacities are functionals of these populations. The functional dependence of the carrying capacities reflects the fact that the correlations between populations can be realized not merely through direct interactions, as in the usual predator-prey Lotka-Volterra model, but also through the influence of species on the carrying capacities of each other. This includes the self-influence of each kind of species on its own carrying capacity with delays. Several examples of such evolution equations with fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1367","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":"2026-05-18T01:57:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8iCB6H9spA+fkB6vCSx+LK/AMy5EPWNME343vfN7ksSvVbTZprIw4awU9uIBVSUKsIqFXyxUzKeKrqtnBYlzDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:36:33.868790Z"},"content_sha256":"cf7db70de382fb8f02d8fdd98d7c83dc9c1202aaa0920ceec71f6b5c0ec4cc92","schema_version":"1.0","event_id":"sha256:cf7db70de382fb8f02d8fdd98d7c83dc9c1202aaa0920ceec71f6b5c0ec4cc92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UAILLCAVVXFKF7HHYSZEZ4OD5P/bundle.json","state_url":"https://pith.science/pith/UAILLCAVVXFKF7HHYSZEZ4OD5P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UAILLCAVVXFKF7HHYSZEZ4OD5P/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":"2026-06-08T18:36:33Z","links":{"resolver":"https://pith.science/pith/UAILLCAVVXFKF7HHYSZEZ4OD5P","bundle":"https://pith.science/pith/UAILLCAVVXFKF7HHYSZEZ4OD5P/bundle.json","state":"https://pith.science/pith/UAILLCAVVXFKF7HHYSZEZ4OD5P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UAILLCAVVXFKF7HHYSZEZ4OD5P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UAILLCAVVXFKF7HHYSZEZ4OD5P","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":"97b92840217289824f914395a3988487d99b03def5e244039ae1ce2b209ddeee","cross_cats_sorted":["physics.bio-ph","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2012-05-07T12:56:10Z","title_canon_sha256":"c4199b1aca7cd681257f60c43015feab06984d1cde70b3140edd59c262b331ed"},"schema_version":"1.0","source":{"id":"1205.1367","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1367","created_at":"2026-05-18T01:57:37Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1367v1","created_at":"2026-05-18T01:57:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1367","created_at":"2026-05-18T01:57:37Z"},{"alias_kind":"pith_short_12","alias_value":"UAILLCAVVXFK","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UAILLCAVVXFKF7HH","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UAILLCAV","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:cf7db70de382fb8f02d8fdd98d7c83dc9c1202aaa0920ceec71f6b5c0ec4cc92","target":"graph","created_at":"2026-05-18T01:57:37Z","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":"A class of models is introduced describing the evolution of population species whose carrying capacities are functionals of these populations. The functional dependence of the carrying capacities reflects the fact that the correlations between populations can be realized not merely through direct interactions, as in the usual predator-prey Lotka-Volterra model, but also through the influence of species on the carrying capacities of each other. This includes the self-influence of each kind of species on its own carrying capacity with delays. Several examples of such evolution equations with fun","authors_text":"D. Sornette, E. P. Yukalova, V. I. Yukalov","cross_cats":["physics.bio-ph","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2012-05-07T12:56:10Z","title":"Extreme events in population dynamics with functional carrying capacity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1367","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":"sha256:48847f7db3affe0ed99f590db913041dac083df0be3b80a0708c60d0c3a5996a","target":"record","created_at":"2026-05-18T01:57:37Z","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":"97b92840217289824f914395a3988487d99b03def5e244039ae1ce2b209ddeee","cross_cats_sorted":["physics.bio-ph","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2012-05-07T12:56:10Z","title_canon_sha256":"c4199b1aca7cd681257f60c43015feab06984d1cde70b3140edd59c262b331ed"},"schema_version":"1.0","source":{"id":"1205.1367","kind":"arxiv","version":1}},"canonical_sha256":"a010b58815adcaa2fce7c4b24cf1c3ebd98a7d43d7184ef2a5debc97876cf4bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a010b58815adcaa2fce7c4b24cf1c3ebd98a7d43d7184ef2a5debc97876cf4bb","first_computed_at":"2026-05-18T01:57:37.343087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:37.343087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"icHsYsPf3riNW9tq5ISkAdd37fAIZmmasyBQTpTR2JEat/VF2v2gl+cpboMV+ygf0abWOWX9IHEk/DDyhkNQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:37.343829Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1367","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48847f7db3affe0ed99f590db913041dac083df0be3b80a0708c60d0c3a5996a","sha256:cf7db70de382fb8f02d8fdd98d7c83dc9c1202aaa0920ceec71f6b5c0ec4cc92"],"state_sha256":"cba57f89f5839e5d37dd9dc9c5924dc012ce2dbc5c515fa251f1e578698aa481"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t4vP0eVyyOHjhzuIYX/S5LXFe1+Swb3LwuUQAjfZz++2etuQyvl11bM035J34eQRfxCr/ws/SfcLat1OWjvpAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:36:33.872796Z","bundle_sha256":"8f36de9bb674b6fd390a637d8c8966d2bc773046f2281441aaf1fe72ddb25c3e"}}