{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DFPZVMIBHDIO47RXFNBDZWAAHE","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":"724884bc66bdfb31ce29e31608e3bf0c7687c7e33b3c1a776e027bdf7c9ae9a4","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-10T13:59:30Z","title_canon_sha256":"da65d7d472e71e8f04a45c25ca0ca409f15113f8ac77eab085aa74e5ca70c726"},"schema_version":"1.0","source":{"id":"1207.2355","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2355","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2355v1","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2355","created_at":"2026-05-18T03:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"DFPZVMIBHDIO","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DFPZVMIBHDIO47RX","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DFPZVMIB","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:ec2a7896ab3f6a437f1486039e9b113f5edc17ccbb3ed8c513d152206b0098f8","target":"graph","created_at":"2026-05-18T03:51:24Z","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":"Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena of front acceleration (when the motility is unbounded) as well as other quantitative results, such as the selection of the most motile individuals (when the motility is bounded). The key argument for the construction and analysis of traveling fronts is the derivation of the dispersion relation linking the speed of the wave and the spatial decay. When the mot","authors_text":"Benoit Perthame (INRIA Rocquencourt, Emeric Bouin (UMPA-ENSL), Gael Raoul (CEFE), LJLL), Nicolas Meunier (MAP5), Raphael Voituriez (LPTMC), Sepideh Mirrahimi (CMAP), Vincent Calvez (UMPA-ENSL)","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-10T13:59:30Z","title":"Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2355","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":"sha256:058214beb6b84b3a9633805b3cf83219d2c756985a2090b11de19edc45fd76d3","target":"record","created_at":"2026-05-18T03:51:24Z","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":"724884bc66bdfb31ce29e31608e3bf0c7687c7e33b3c1a776e027bdf7c9ae9a4","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-10T13:59:30Z","title_canon_sha256":"da65d7d472e71e8f04a45c25ca0ca409f15113f8ac77eab085aa74e5ca70c726"},"schema_version":"1.0","source":{"id":"1207.2355","kind":"arxiv","version":1}},"canonical_sha256":"195f9ab10138d0ee7e372b423cd80039322698d66c519d52eb88d3e9aa53f44b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"195f9ab10138d0ee7e372b423cd80039322698d66c519d52eb88d3e9aa53f44b","first_computed_at":"2026-05-18T03:51:24.304980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:24.304980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2QxDMsdvigFdjAGADcHPedBUZMArtHhq8iD/CpTj8C+Bw+qtZconHFrT/F2SJT8QjnI3Bd+Q9LxQKmiPZez3CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:24.305705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.2355","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:058214beb6b84b3a9633805b3cf83219d2c756985a2090b11de19edc45fd76d3","sha256:ec2a7896ab3f6a437f1486039e9b113f5edc17ccbb3ed8c513d152206b0098f8"],"state_sha256":"086d4da1abb97da8734ddfda99c960f2585df81c6ca7ebc87ab74b47d3ae50ec"}