{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PK7VWQU7MCPNPRFKSQLAIH54C7","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":"d05490e1dd3728da5281cab72e1b4f6ce7aee5e9204fd64fb9474f1f771cbcc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-30T14:38:31Z","title_canon_sha256":"9192bda3320e839b6f8795b843cfd02f9e0fedc51666f8879d288be245581829"},"schema_version":"1.0","source":{"id":"1007.5462","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.5462","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1007.5462v1","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.5462","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"PK7VWQU7MCPN","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PK7VWQU7MCPNPRFK","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PK7VWQU7","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:83274c19e0acdd5b88db978475d4880886766d0e453f6795c18c7ea1422b81ca","target":"graph","created_at":"2026-05-18T04:42:45Z","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 study two types of stochastic processes, a mean-field spatial system of interacting Fisher-Wright diffusions with an inferior and an advantageous type with rare mutation (inferior to advantageous) and a (mean-field) spatial system of supercritical branching random walks with an additional deathrate which is quadratic in the local number of particles. The former describes a standard two-type population under selection, mutation, the latter models describe a population under scarce resources causing additional death at high local population intensity. Geographic space is modelled by $\\{1, \\cd","authors_text":"Andreas Greven, Donald A. Dawson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-30T14:38:31Z","title":"Multiscale analysis: Fisher-Wright diffusions with rare mutations and selection, logistic branching system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.5462","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":"sha256:7cda2fa61cd1b64bfff5d779775eae33084c5d9c113b5e6e1b55f706ddf8f0be","target":"record","created_at":"2026-05-18T04:42:45Z","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":"d05490e1dd3728da5281cab72e1b4f6ce7aee5e9204fd64fb9474f1f771cbcc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-30T14:38:31Z","title_canon_sha256":"9192bda3320e839b6f8795b843cfd02f9e0fedc51666f8879d288be245581829"},"schema_version":"1.0","source":{"id":"1007.5462","kind":"arxiv","version":1}},"canonical_sha256":"7abf5b429f609ed7c4aa9416041fbc17cf8eb67d86eaa867eb830ad817028d68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7abf5b429f609ed7c4aa9416041fbc17cf8eb67d86eaa867eb830ad817028d68","first_computed_at":"2026-05-18T04:42:45.178761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:45.178761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jvz9fQM+KlgontJ8Cf/ibir++qa9qyEsVZdFeQqtHTTI64rEJ2bNPoUrN69lDFLj+B6laQaiZ3XPHleA7UMDDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:45.179294Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.5462","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cda2fa61cd1b64bfff5d779775eae33084c5d9c113b5e6e1b55f706ddf8f0be","sha256:83274c19e0acdd5b88db978475d4880886766d0e453f6795c18c7ea1422b81ca"],"state_sha256":"ebd1c17ce94d031885049070de1a54f951ae86f64c458f9217f26da18ace8cd5"}