{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:LLFPGWAJGO4HHIMJ3J4LMNHMSX","short_pith_number":"pith:LLFPGWAJ","canonical_record":{"source":{"id":"1111.6460","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-28T14:55:32Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"d009d28fced607e23aee44e63f6a37d4189be391dd31f803b39e29884edc1699","abstract_canon_sha256":"9884675ef87ae1b8945d660945a32c8b215309a8cb0b74704d91943b9db48d5a"},"schema_version":"1.0"},"canonical_sha256":"5acaf3580933b873a189da78b634ec95d5815a2e6f748eaef3c2e9ab3f80d195","source":{"kind":"arxiv","id":"1111.6460","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6460","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6460v1","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6460","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"LLFPGWAJGO4H","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LLFPGWAJGO4HHIMJ","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LLFPGWAJ","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:LLFPGWAJGO4HHIMJ3J4LMNHMSX","target":"record","payload":{"canonical_record":{"source":{"id":"1111.6460","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-28T14:55:32Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"d009d28fced607e23aee44e63f6a37d4189be391dd31f803b39e29884edc1699","abstract_canon_sha256":"9884675ef87ae1b8945d660945a32c8b215309a8cb0b74704d91943b9db48d5a"},"schema_version":"1.0"},"canonical_sha256":"5acaf3580933b873a189da78b634ec95d5815a2e6f748eaef3c2e9ab3f80d195","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:29.883754Z","signature_b64":"y5JtOrEvDjIw54xC/c4TF8mK15GekKDRTcraY/Hvd35Bk71vkDjTQzpH5loqWPNFPJ8pcz0kaM05jHrslb73Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5acaf3580933b873a189da78b634ec95d5815a2e6f748eaef3c2e9ab3f80d195","last_reissued_at":"2026-05-18T04:07:29.882901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:29.882901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.6460","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":"2026-05-18T04:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Z2YFAMZrCaw2PeA3RFn3iHg2d9xnKLWK7/ILFnkuvN2cpuBj8HioSiSYyNMBuQX1EnOzmZkeopRguKCWO0uCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:04:59.644709Z"},"content_sha256":"6b82bdd9755d3cab77c6d2f773bff055b3308b6eab45edc1e2705918e8013989","schema_version":"1.0","event_id":"sha256:6b82bdd9755d3cab77c6d2f773bff055b3308b6eab45edc1e2705918e8013989"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:LLFPGWAJGO4HHIMJ3J4LMNHMSX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effect of population size in a Prey-Predator model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"math.DS","authors_text":"Claude Lobry (INRIA Sophia Antipolis), Fabien Campillo (INRIA Sophia Antipolis, MISTEA)","submitted_at":"2011-11-28T14:55:32Z","abstract_excerpt":"We consider a stochastic version of the basic predator-prey differential equation model. The model, which contains a parameter \\omega which represents the number of individuals for one unit of prey -- If x denotes the quantity of prey in the differential equation model x = 1 means that there are \\omega individuals in the discontinuous one -- is derived from the classical birth and death process. It is shown by the mean of simulations and explained by a mathematical analysis based on results in singular perturbation theory (the so called theory of Canards) that qualitative properties of the mod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6460","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":"2026-05-18T04:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2K+CwF031Gm/Jdem7oH9lMV7F+6MQlWa0OJYaBPmY70/+7QEmea8mZmZrjweVDfVNGyASW8PBSKwCl5JdkciBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:04:59.645364Z"},"content_sha256":"349048169175cff81f576104f2ce4af2a2c30ca228b313eeb2ac5a7859bf18e8","schema_version":"1.0","event_id":"sha256:349048169175cff81f576104f2ce4af2a2c30ca228b313eeb2ac5a7859bf18e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LLFPGWAJGO4HHIMJ3J4LMNHMSX/bundle.json","state_url":"https://pith.science/pith/LLFPGWAJGO4HHIMJ3J4LMNHMSX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LLFPGWAJGO4HHIMJ3J4LMNHMSX/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":"2026-05-28T19:04:59Z","links":{"resolver":"https://pith.science/pith/LLFPGWAJGO4HHIMJ3J4LMNHMSX","bundle":"https://pith.science/pith/LLFPGWAJGO4HHIMJ3J4LMNHMSX/bundle.json","state":"https://pith.science/pith/LLFPGWAJGO4HHIMJ3J4LMNHMSX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LLFPGWAJGO4HHIMJ3J4LMNHMSX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LLFPGWAJGO4HHIMJ3J4LMNHMSX","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":"9884675ef87ae1b8945d660945a32c8b215309a8cb0b74704d91943b9db48d5a","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-28T14:55:32Z","title_canon_sha256":"d009d28fced607e23aee44e63f6a37d4189be391dd31f803b39e29884edc1699"},"schema_version":"1.0","source":{"id":"1111.6460","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6460","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6460v1","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6460","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"LLFPGWAJGO4H","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LLFPGWAJGO4HHIMJ","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LLFPGWAJ","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:349048169175cff81f576104f2ce4af2a2c30ca228b313eeb2ac5a7859bf18e8","target":"graph","created_at":"2026-05-18T04:07:29Z","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":"We consider a stochastic version of the basic predator-prey differential equation model. The model, which contains a parameter \\omega which represents the number of individuals for one unit of prey -- If x denotes the quantity of prey in the differential equation model x = 1 means that there are \\omega individuals in the discontinuous one -- is derived from the classical birth and death process. It is shown by the mean of simulations and explained by a mathematical analysis based on results in singular perturbation theory (the so called theory of Canards) that qualitative properties of the mod","authors_text":"Claude Lobry (INRIA Sophia Antipolis), Fabien Campillo (INRIA Sophia Antipolis, MISTEA)","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-28T14:55:32Z","title":"Effect of population size in a Prey-Predator model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6460","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":"sha256:6b82bdd9755d3cab77c6d2f773bff055b3308b6eab45edc1e2705918e8013989","target":"record","created_at":"2026-05-18T04:07:29Z","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":"9884675ef87ae1b8945d660945a32c8b215309a8cb0b74704d91943b9db48d5a","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-28T14:55:32Z","title_canon_sha256":"d009d28fced607e23aee44e63f6a37d4189be391dd31f803b39e29884edc1699"},"schema_version":"1.0","source":{"id":"1111.6460","kind":"arxiv","version":1}},"canonical_sha256":"5acaf3580933b873a189da78b634ec95d5815a2e6f748eaef3c2e9ab3f80d195","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5acaf3580933b873a189da78b634ec95d5815a2e6f748eaef3c2e9ab3f80d195","first_computed_at":"2026-05-18T04:07:29.882901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:29.882901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y5JtOrEvDjIw54xC/c4TF8mK15GekKDRTcraY/Hvd35Bk71vkDjTQzpH5loqWPNFPJ8pcz0kaM05jHrslb73Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:29.883754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.6460","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b82bdd9755d3cab77c6d2f773bff055b3308b6eab45edc1e2705918e8013989","sha256:349048169175cff81f576104f2ce4af2a2c30ca228b313eeb2ac5a7859bf18e8"],"state_sha256":"47c78984f783a6c82493243a09fb6ac4447083b079a3cd021c56b1cf4550f529"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5OmY9cerwTncAgm4PHjFgVOxNcexlT760JgeaKZ778BBF1ODcLT4FKCe49uIzoqlfjWoB4jEzQnk7s7GrA4kCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T19:04:59.648710Z","bundle_sha256":"fc7f72f0c44cc53383d8070ada4e6a042c575ee262ae42b4a0482961f2b87eca"}}