{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:VSNTKWKMPYBBFI2R5CWOUEHFCV","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":"b70582d41d41c5a3faba9fa3030448870e7741f832eaf7e529c92a1d138da634","cross_cats_sorted":["math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-09-04T07:21:07Z","title_canon_sha256":"e87ce781743036979ed03aa4260eb20cd55e9d47ab896e86e65481e148e63063"},"schema_version":"1.0","source":{"id":"0809.0758","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.0758","created_at":"2026-05-18T02:15:35Z"},{"alias_kind":"arxiv_version","alias_value":"0809.0758v1","created_at":"2026-05-18T02:15:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.0758","created_at":"2026-05-18T02:15:35Z"},{"alias_kind":"pith_short_12","alias_value":"VSNTKWKMPYBB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"VSNTKWKMPYBBFI2R","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"VSNTKWKM","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:72cca19c2e1df599ab280b28ed87e40a80a89133db732b2e6b3ee42533ce18b9","target":"graph","created_at":"2026-05-18T02:15:35Z","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 aim of this paper is to analyze different regulation mechanisms in spatial continuous stochastic development models. We describe the density behavior for models with global mortality and local establishment rates. We prove that the local self-regulation via a competition mechanism (density dependent mortality) may suppress a unbounded growth of the averaged density if the competition kernel is superstable.","authors_text":"Dmitri Finkelshtein, Yuri Kondratiev","cross_cats":["math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-09-04T07:21:07Z","title":"Regulation mechanisms in spatial stochastic development models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.0758","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:dc29e0ace19daec1225a71689b3732f40498b84ea00778d79979f6a0be4c1115","target":"record","created_at":"2026-05-18T02:15:35Z","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":"b70582d41d41c5a3faba9fa3030448870e7741f832eaf7e529c92a1d138da634","cross_cats_sorted":["math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-09-04T07:21:07Z","title_canon_sha256":"e87ce781743036979ed03aa4260eb20cd55e9d47ab896e86e65481e148e63063"},"schema_version":"1.0","source":{"id":"0809.0758","kind":"arxiv","version":1}},"canonical_sha256":"ac9b35594c7e0212a351e8acea10e5155e59169ff82b91600c19afc72e70aebf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac9b35594c7e0212a351e8acea10e5155e59169ff82b91600c19afc72e70aebf","first_computed_at":"2026-05-18T02:15:35.557108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:35.557108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"enfvJbTO8RAOyHiOrcxsZG/S8dlk7bVwLCAtO6/abD2Wpu3l/fY7K9WJbYC4MrNjtaGdcFuVglR2CkDnh52sBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:35.557801Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.0758","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc29e0ace19daec1225a71689b3732f40498b84ea00778d79979f6a0be4c1115","sha256:72cca19c2e1df599ab280b28ed87e40a80a89133db732b2e6b3ee42533ce18b9"],"state_sha256":"76e204b9377df719bbda130a8f9055337c4be548a49d1751699baf8422ffca5e"}