{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6TGYK75DUFCVQ65O2P72QRJO3W","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":"f4d0f8715538b0805a00394fd6b78d4f699555f2d0289d1241fc2bb0557839af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-02T07:26:26Z","title_canon_sha256":"38ce37f8d16331eadd5f97879ba2639f533cfb1cc4409f38a1caa49caa28e8e5"},"schema_version":"1.0","source":{"id":"1111.0408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0408","created_at":"2026-05-18T04:09:45Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0408v1","created_at":"2026-05-18T04:09:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0408","created_at":"2026-05-18T04:09:45Z"},{"alias_kind":"pith_short_12","alias_value":"6TGYK75DUFCV","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6TGYK75DUFCVQ65O","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6TGYK75D","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:8c89bf7d4fbcddae51c79089bb56bbfefc0f928ca1f7b98e8600fe02af610a56","target":"graph","created_at":"2026-05-18T04:09:45Z","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 the Fisher-KPP equation with a fractional laplacian of order {\\alpha} \\in (0, 1). We know that the stable state invades the unstable one at constant speed for {\\alpha} = 1, and at an exponential in time velocity for {\\alpha} \\in (0, 1). The transition between these two different speeds is examined in this paper. We prove that during a time of the order - ln(1 - {\\alpha}), the propagation is linear and then it is exponential.","authors_text":"Anne-Charline Coulon, Jean-Michel Roquejoffre","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-02T07:26:26Z","title":"Transition between linear and exponential propagation in Fisher-KPP type reaction-diffusion equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0408","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":"sha256:76c64187643d9077dc56af9761120266532ec2681f6c6c6ec62d7b70512e03cc","target":"record","created_at":"2026-05-18T04:09:45Z","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":"f4d0f8715538b0805a00394fd6b78d4f699555f2d0289d1241fc2bb0557839af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-02T07:26:26Z","title_canon_sha256":"38ce37f8d16331eadd5f97879ba2639f533cfb1cc4409f38a1caa49caa28e8e5"},"schema_version":"1.0","source":{"id":"1111.0408","kind":"arxiv","version":1}},"canonical_sha256":"f4cd857fa3a145587baed3ffa8452edd8238d2665e0749817c4befd9fb38aa3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4cd857fa3a145587baed3ffa8452edd8238d2665e0749817c4befd9fb38aa3e","first_computed_at":"2026-05-18T04:09:45.042874Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:45.042874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d2EV8MxHE4aMm6umULHdnBcmvUvbJrJn8ifgICxmm/2dyCtMZwd73lQN+AnLJigJsbqE3K7qkwqvg0gnZxzeCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:45.043452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.0408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76c64187643d9077dc56af9761120266532ec2681f6c6c6ec62d7b70512e03cc","sha256:8c89bf7d4fbcddae51c79089bb56bbfefc0f928ca1f7b98e8600fe02af610a56"],"state_sha256":"861d38f46e3ed970b2630f1cb7c0dc233d3c11ff2b173f92f90395bcd5b73335"}