{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NV2YDX6EITJC7DMJQ7YCX5GONS","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":"938728eae10e86a607ffcbe66785a78772348ab27880138d177f746f82093e68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-05T14:56:34Z","title_canon_sha256":"70c0da06e03d9dc59efc2cf9fa085b4d7c39fb6ee0a80e98938960f294947753"},"schema_version":"1.0","source":{"id":"1302.1053","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1053","created_at":"2026-05-18T03:34:26Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1053v1","created_at":"2026-05-18T03:34:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1053","created_at":"2026-05-18T03:34:26Z"},{"alias_kind":"pith_short_12","alias_value":"NV2YDX6EITJC","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NV2YDX6EITJC7DMJ","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NV2YDX6E","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:2cd87e2394e0f53e762966f92dcd7ce397eb75c2f47d3b384032cb46743b06dd","target":"graph","created_at":"2026-05-18T03:34:26Z","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":"In this paper we are interested in propagation phenomena for nonlocal reaction-diffusion equations of the type: $\\delta_tu = J \\times u - u + f (x, u) t \\in R^+, x \\in R^N$, where J is a probability density and f is a KPP nonlinearity periodic in the x variables. Under suitable assumptions we establish the existence of pulsating fronts describing the invasion of the 0 state by a heterogeneous state. We also give a variational characterization of the minimal speed of such pulsating fronts and exponential bounds on the asymptotic behavior of the solution.","authors_text":"CMM), Jerome Coville (BIOSP), Juan Davila (DIM, Salome Martinez (DIM","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-05T14:56:34Z","title":"Pulsating fronts for nonlocal dispersion and KPP nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1053","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":"sha256:902da95ccac82e5646a3289f91cd2a238807fd1b1ab63bf369cfeee1555d0095","target":"record","created_at":"2026-05-18T03:34:26Z","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":"938728eae10e86a607ffcbe66785a78772348ab27880138d177f746f82093e68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-05T14:56:34Z","title_canon_sha256":"70c0da06e03d9dc59efc2cf9fa085b4d7c39fb6ee0a80e98938960f294947753"},"schema_version":"1.0","source":{"id":"1302.1053","kind":"arxiv","version":1}},"canonical_sha256":"6d7581dfc444d22f8d8987f02bf4ce6ca1900358607771d2180214335bbbc007","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d7581dfc444d22f8d8987f02bf4ce6ca1900358607771d2180214335bbbc007","first_computed_at":"2026-05-18T03:34:26.292448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:26.292448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sqx8UqJ2j7WQg980KbTXo3vyQO2OuAIdUeCPmKRCLY6ZjM82I8yVGgq0kQ2QpORCvh9gZSbFNO04ipCp2h/8BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:26.293330Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.1053","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:902da95ccac82e5646a3289f91cd2a238807fd1b1ab63bf369cfeee1555d0095","sha256:2cd87e2394e0f53e762966f92dcd7ce397eb75c2f47d3b384032cb46743b06dd"],"state_sha256":"f8701b126a931629ccaa32658b8110ccde53e9de0e5a7b38aa594cab14ed0a63"}