{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:JB3D7YWXZYSV6ABU5F7NBJVM3A","short_pith_number":"pith:JB3D7YWX","schema_version":"1.0","canonical_sha256":"48763fe2d7ce255f0034e97ed0a6acd81595a2e94d80d8af237a12373b5370dc","source":{"kind":"arxiv","id":"0906.4538","version":1},"attestation_state":"computed","paper":{"title":"The one-dimensional Keller-Segel model with fractional diffusion of cells","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nikolaos Bournaveas, Vincent Calvez (DMA)","submitted_at":"2009-06-24T18:36:32Z","abstract_excerpt":"We investigate the one-dimensional Keller-Segel model where the diffusion is replaced by a non-local operator, namely the fractional diffusion with exponent $0<\\alpha\\leq 2$. We prove some features related to the classical two-dimensional Keller-Segel system: blow-up may or may not occur depending on the initial data. More precisely a singularity appears in finite time when $\\alpha<1$ and the initial configuration of cells is sufficiently concentrated. On the opposite, global existence holds true for $\\alpha\\leq1$ if the initial density is small enough in the sense of the $L^{1/\\alpha}$ norm."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0906.4538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-06-24T18:36:32Z","cross_cats_sorted":[],"title_canon_sha256":"2c5280f27c6a5e64d10a50092f60c6185a4febdd3f8d3eb21ca0c1ce23e745d9","abstract_canon_sha256":"cea4c77e1457ccd2d439db2bd91df96da6224766d4d182f517767729aba059d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:12.914672Z","signature_b64":"GO4xCPUBOlh8qepKVxhS4GhWJWOTO6ia2EKltPwQIAaEO+9EhzAsQ1PVap4Maq7Q8XWvHgPAH8MKbnCgQuSBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48763fe2d7ce255f0034e97ed0a6acd81595a2e94d80d8af237a12373b5370dc","last_reissued_at":"2026-05-18T02:13:12.914285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:12.914285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The one-dimensional Keller-Segel model with fractional diffusion of cells","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nikolaos Bournaveas, Vincent Calvez (DMA)","submitted_at":"2009-06-24T18:36:32Z","abstract_excerpt":"We investigate the one-dimensional Keller-Segel model where the diffusion is replaced by a non-local operator, namely the fractional diffusion with exponent $0<\\alpha\\leq 2$. We prove some features related to the classical two-dimensional Keller-Segel system: blow-up may or may not occur depending on the initial data. More precisely a singularity appears in finite time when $\\alpha<1$ and the initial configuration of cells is sufficiently concentrated. On the opposite, global existence holds true for $\\alpha\\leq1$ if the initial density is small enough in the sense of the $L^{1/\\alpha}$ norm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.4538","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"0906.4538","created_at":"2026-05-18T02:13:12.914353+00:00"},{"alias_kind":"arxiv_version","alias_value":"0906.4538v1","created_at":"2026-05-18T02:13:12.914353+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.4538","created_at":"2026-05-18T02:13:12.914353+00:00"},{"alias_kind":"pith_short_12","alias_value":"JB3D7YWXZYSV","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"JB3D7YWXZYSV6ABU","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"JB3D7YWX","created_at":"2026-05-18T12:26:00.592388+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JB3D7YWXZYSV6ABU5F7NBJVM3A","json":"https://pith.science/pith/JB3D7YWXZYSV6ABU5F7NBJVM3A.json","graph_json":"https://pith.science/api/pith-number/JB3D7YWXZYSV6ABU5F7NBJVM3A/graph.json","events_json":"https://pith.science/api/pith-number/JB3D7YWXZYSV6ABU5F7NBJVM3A/events.json","paper":"https://pith.science/paper/JB3D7YWX"},"agent_actions":{"view_html":"https://pith.science/pith/JB3D7YWXZYSV6ABU5F7NBJVM3A","download_json":"https://pith.science/pith/JB3D7YWXZYSV6ABU5F7NBJVM3A.json","view_paper":"https://pith.science/paper/JB3D7YWX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0906.4538&json=true","fetch_graph":"https://pith.science/api/pith-number/JB3D7YWXZYSV6ABU5F7NBJVM3A/graph.json","fetch_events":"https://pith.science/api/pith-number/JB3D7YWXZYSV6ABU5F7NBJVM3A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JB3D7YWXZYSV6ABU5F7NBJVM3A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JB3D7YWXZYSV6ABU5F7NBJVM3A/action/storage_attestation","attest_author":"https://pith.science/pith/JB3D7YWXZYSV6ABU5F7NBJVM3A/action/author_attestation","sign_citation":"https://pith.science/pith/JB3D7YWXZYSV6ABU5F7NBJVM3A/action/citation_signature","submit_replication":"https://pith.science/pith/JB3D7YWXZYSV6ABU5F7NBJVM3A/action/replication_record"}},"created_at":"2026-05-18T02:13:12.914353+00:00","updated_at":"2026-05-18T02:13:12.914353+00:00"}