{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6HUINFGN7ED2RJBELVWUCWCDPK","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":"828ac526a231e6e7deb1ba7985eb814899900397e6e52fa938d8a8ee4a294c7c","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-07-07T16:23:47Z","title_canon_sha256":"1fa4ccd9284823f1a91756a6f06ad1306157455e50d2471493209ea041264d7e"},"schema_version":"1.0","source":{"id":"1407.1759","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1759","created_at":"2026-05-18T02:41:09Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1759v2","created_at":"2026-05-18T02:41:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1759","created_at":"2026-05-18T02:41:09Z"},{"alias_kind":"pith_short_12","alias_value":"6HUINFGN7ED2","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6HUINFGN7ED2RJBE","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6HUINFGN","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:7aa9ce3ebfcf2d0fb3d93741c62e7e10b38390b45140686402f9703cbf0d4a1d","target":"graph","created_at":"2026-05-18T02:41:09Z","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 develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit of large system sizes is shown to be very well-approximated by a Fokker-Planck-like equation, or equivalently by a set of stochastic difference equations. This formalism is applied to the specific case of two species: one predator species and its prey species. Quasi-cycles --- stochastic cycles sustained and amplified by the demographic noise --- previously f","authors_text":"Alan J. McKane, C\\'esar Parra-Rojas, Duccio Fanelli, Joseph D. Challenger","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-07-07T16:23:47Z","title":"Intrinsic noise and two-dimensional maps: Quasicycles, quasiperiodicity, and chaos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1759","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":"sha256:18f375dd3da0d50d422d320afb85e351d49f5170941e80f3d974ed5ad313689b","target":"record","created_at":"2026-05-18T02:41:09Z","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":"828ac526a231e6e7deb1ba7985eb814899900397e6e52fa938d8a8ee4a294c7c","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-07-07T16:23:47Z","title_canon_sha256":"1fa4ccd9284823f1a91756a6f06ad1306157455e50d2471493209ea041264d7e"},"schema_version":"1.0","source":{"id":"1407.1759","kind":"arxiv","version":2}},"canonical_sha256":"f1e88694cdf907a8a4245d6d4158437ab0b17265172ba2c4d8d9b465f0fd4d29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1e88694cdf907a8a4245d6d4158437ab0b17265172ba2c4d8d9b465f0fd4d29","first_computed_at":"2026-05-18T02:41:09.987106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:09.987106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VLQG1dCeY/TrVQjFfkKkJrP3i2A1R1PbtJjZATsuR66KZopgfClORToa5J9DolcTQLuvu8QuJ6LaS8WWlUeEDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:09.987529Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1759","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18f375dd3da0d50d422d320afb85e351d49f5170941e80f3d974ed5ad313689b","sha256:7aa9ce3ebfcf2d0fb3d93741c62e7e10b38390b45140686402f9703cbf0d4a1d"],"state_sha256":"6ba8b3689012f7df5d7c2594c06b94b8eace2e327ba05697ffdfa10b3db08fe9"}