{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LZ27TVR5U2YTS3TTTFVUELEEMH","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":"a4a44f84c93c410cca6807982abe1e7c9300d46354f8cf23c22151d626c77e4d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2013-04-08T19:23:20Z","title_canon_sha256":"b2949eea8faa144423015224f72a965d5c03fe18c8b8916af00c963a027cbd93"},"schema_version":"1.0","source":{"id":"1304.2324","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2324","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2324v1","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2324","created_at":"2026-05-18T03:28:43Z"},{"alias_kind":"pith_short_12","alias_value":"LZ27TVR5U2YT","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LZ27TVR5U2YTS3TT","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LZ27TVR5","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:1b4302be8bb3662eddb33248e5531d5d5f0a2d3ec7ee0f88579e8c5f57efb466","target":"graph","created_at":"2026-05-18T03:28:43Z","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 phase space theory for population dynamics in Ecology is presented. This theory applies for a certain class of dynamical systems, that will be called M-systems, for which a conserved quantity, the M-function, can be defined in phase space. This M-function is the generator of time displacements and contains all the dynamical information of the system. In this sense the M-function plays the role of the hamiltonian function for mechanical systems. In analogy with Hamilton theory we derive equations of motion as derivatives over the resource function in phase space. A M-bracket is defined which ","authors_text":"Jesus Martinez-Linares","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2013-04-08T19:23:20Z","title":"Phase Space Formulation of Population Dynamics in Ecology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2324","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:b2410e36b5190c7e7a55354a46498dcc51b49c55ccd405cade74c8c27479135b","target":"record","created_at":"2026-05-18T03:28:43Z","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":"a4a44f84c93c410cca6807982abe1e7c9300d46354f8cf23c22151d626c77e4d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2013-04-08T19:23:20Z","title_canon_sha256":"b2949eea8faa144423015224f72a965d5c03fe18c8b8916af00c963a027cbd93"},"schema_version":"1.0","source":{"id":"1304.2324","kind":"arxiv","version":1}},"canonical_sha256":"5e75f9d63da6b1396e73996b422c8461ef0b75d52c4f3327fe39da6c131e8f09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e75f9d63da6b1396e73996b422c8461ef0b75d52c4f3327fe39da6c131e8f09","first_computed_at":"2026-05-18T03:28:43.404813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:43.404813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rg90VpMdh+IFlVoApdT56VMrowqpVr5IlVEdgHUionw43Z1AScXAWcicr58eWvCYHnzNRbPcM84LdtWLqZvFAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:43.405475Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2324","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2410e36b5190c7e7a55354a46498dcc51b49c55ccd405cade74c8c27479135b","sha256:1b4302be8bb3662eddb33248e5531d5d5f0a2d3ec7ee0f88579e8c5f57efb466"],"state_sha256":"6e00bde51b6ab3c8dd251432b99b0ed369470d4a57a54c1f5a07ddef76ac728e"}