{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3KFJLGEUSRC3P5ONQWSPWO6C5P","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":"af455c646412da2051f8c3db9e2b54d6663d53d03a00b9a1724cc6fa2f9c3c56","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-31T14:35:10Z","title_canon_sha256":"1b7dd1d4fda31b9d162f98fe17f978d77cbd35fb03d71d5b2316775af502c50d"},"schema_version":"1.0","source":{"id":"1307.8332","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.8332","created_at":"2026-05-18T03:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1307.8332v1","created_at":"2026-05-18T03:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.8332","created_at":"2026-05-18T03:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"3KFJLGEUSRC3","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3KFJLGEUSRC3P5ON","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3KFJLGEU","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:33a552c8f5f135ef1966dd1dd05d78b734b085fe76baf4f5b0e65901876c059d","target":"graph","created_at":"2026-05-18T03:17:01Z","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 a non-local parabolic Lotka-Volterra type equation describing a population structured by a space variable x 2 Rd and a phenotypical trait 2 . Considering diffusion, mutations and space-local competition between the individuals, we analyze the asymptotic (long- time/long-range in the x variable) exponential behavior of the solutions. Using some kind of real phase WKB ansatz, we prove that the propagation of the population in space can be described by a Hamilton-Jacobi equation with obstacle which is independent of . The effective Hamiltonian is derived from an eigenvalue problem. The m","authors_text":"Emeric Bouin (UMPA-ENSL), Sepideh Mirrahimi (IMT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-31T14:35:10Z","title":"A Hamilton-Jacobi approach for a model of population structured by space and trait"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8332","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:e956f6d564935bcf6beff9e1deb6b36bf25206f9b0fa37e774a30e9f1d01b602","target":"record","created_at":"2026-05-18T03:17:01Z","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":"af455c646412da2051f8c3db9e2b54d6663d53d03a00b9a1724cc6fa2f9c3c56","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-31T14:35:10Z","title_canon_sha256":"1b7dd1d4fda31b9d162f98fe17f978d77cbd35fb03d71d5b2316775af502c50d"},"schema_version":"1.0","source":{"id":"1307.8332","kind":"arxiv","version":1}},"canonical_sha256":"da8a9598949445b7f5cd85a4fb3bc2ebf4ca258c4ad2b027e453ccc56c892186","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da8a9598949445b7f5cd85a4fb3bc2ebf4ca258c4ad2b027e453ccc56c892186","first_computed_at":"2026-05-18T03:17:01.525404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:01.525404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2xg0qI9r9x2oQPG+FkXqIkq0BmsnePa+WGznmZ0ECFAzBNx1eUcXCTDLr3BwUrMQmXVZBaosZbDlrIbz5EHcCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:01.526179Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.8332","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e956f6d564935bcf6beff9e1deb6b36bf25206f9b0fa37e774a30e9f1d01b602","sha256:33a552c8f5f135ef1966dd1dd05d78b734b085fe76baf4f5b0e65901876c059d"],"state_sha256":"6344187aa0970bed9032ffc53cd2c7758046dfbbf41bd9c02b25d2992c8ce3e0"}