{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XIA5DIYKZEKVP2KUMZMIEK6YRC","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":"8848b929a2aa5a93ff916b47825652b85e7773e02bd59328ecb2c98f80820c35","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-21T13:03:50Z","title_canon_sha256":"00a5cd5e45ad3037e9228581f42f1ab0cdcef1082f2c179f8e8ba100dcdbd849"},"schema_version":"1.0","source":{"id":"1209.4809","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4809","created_at":"2026-05-18T03:45:01Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4809v1","created_at":"2026-05-18T03:45:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4809","created_at":"2026-05-18T03:45:01Z"},{"alias_kind":"pith_short_12","alias_value":"XIA5DIYKZEKV","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XIA5DIYKZEKVP2KU","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XIA5DIYK","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:1356633fd9eb265383c4e8615380d7e3881c3f373e931b744b39bb3060e38432","target":"graph","created_at":"2026-05-18T03:45:01Z","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 are interested in the time asymptotic location of the level sets of solutions to Fisher-KPP reaction-diffusion equations with fractional diffusion in periodic media. We show that the speed of propagation is exponential in time, with a precise exponent depending on a periodic principal eigenvalue, and that it does not depend on the space direction. This is in contrast with the Freidlin-G\\\"artner formula for the standard Laplacian.","authors_text":"Anne-Charline Coulon, Jean-Michel Roquejoffre, Xavier Cabre","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-21T13:03:50Z","title":"Propagation in Fisher-KPP type equations with fractional diffusion in periodic media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4809","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":"sha256:8ee86ac668bd66024ddce1833ee831d0a11daf222c1e405e874d1bb57d82ed26","target":"record","created_at":"2026-05-18T03:45:01Z","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":"8848b929a2aa5a93ff916b47825652b85e7773e02bd59328ecb2c98f80820c35","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-21T13:03:50Z","title_canon_sha256":"00a5cd5e45ad3037e9228581f42f1ab0cdcef1082f2c179f8e8ba100dcdbd849"},"schema_version":"1.0","source":{"id":"1209.4809","kind":"arxiv","version":1}},"canonical_sha256":"ba01d1a30ac91557e9546658822bd888b300204132facdf025fdba86b5df65ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba01d1a30ac91557e9546658822bd888b300204132facdf025fdba86b5df65ec","first_computed_at":"2026-05-18T03:45:01.734217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:01.734217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wCE7V1VWsDbf6fgfbLCcjeHMmqA25ZMiU6TxPGsZgnJodLwzAQhtclTpwG9kuFMqsZt2pEeovoYgu+sPAlHFDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:01.734963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4809","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ee86ac668bd66024ddce1833ee831d0a11daf222c1e405e874d1bb57d82ed26","sha256:1356633fd9eb265383c4e8615380d7e3881c3f373e931b744b39bb3060e38432"],"state_sha256":"2a3c283a7e62c546d23e08be8e75456f5e3e3ccfad221ff8c2d107b530f49273"}