{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:VICMN4WW2KCJ5C62JAIAVVSHMP","short_pith_number":"pith:VICMN4WW","schema_version":"1.0","canonical_sha256":"aa04c6f2d6d2849e8bda48100ad64763f56ffcbb0ee4547c17ad09ec1f6e79be","source":{"kind":"arxiv","id":"1311.0150","version":2},"attestation_state":"computed","paper":{"title":"Exact criterion for global existence and blow up to a degenerate Keller-Segel system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jinhuan Wang, Li Chen","submitted_at":"2013-11-01T11:46:42Z","abstract_excerpt":"A degenerate Keller-Segel system with diffusion exponent $2n/(n+2)<m<2-\\frac{2}{n}$ in multi dimension is studied. An exact criterion for global existence and blow up of solution is obtained. The estimates on $L^{2n/(n+2)}$ norm of the solution play important roles in our analysis. These estimates are closely related to the optimal constant in Haddy- Littlewood- Sobolev inequality. In the case of initial free energy less than a universal constant which depends on the inverse of total mass, there exists a constant such that if the $L^{2n/(n+2)}$ norm of initial data is less than this constant, "},"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":"1311.0150","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-11-01T11:46:42Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6437b93c988fd188d70b74a1f91940641fb28079dd5bf44d0139f145b01b5539","abstract_canon_sha256":"21c27c50088d54aa3029ea3c859240c6ccb68a1f03d58308039a32dd3f98e89f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:57.353461Z","signature_b64":"/V0+36rKjEpobaNHdl5ULM0zTTHToi43ZHok2APaK1wlm1VCmqhAMjAJEGie3I1KvGqQc859G3/VV9qRMCifBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa04c6f2d6d2849e8bda48100ad64763f56ffcbb0ee4547c17ad09ec1f6e79be","last_reissued_at":"2026-05-18T03:05:57.352756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:57.352756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact criterion for global existence and blow up to a degenerate Keller-Segel system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jinhuan Wang, Li Chen","submitted_at":"2013-11-01T11:46:42Z","abstract_excerpt":"A degenerate Keller-Segel system with diffusion exponent $2n/(n+2)<m<2-\\frac{2}{n}$ in multi dimension is studied. An exact criterion for global existence and blow up of solution is obtained. The estimates on $L^{2n/(n+2)}$ norm of the solution play important roles in our analysis. These estimates are closely related to the optimal constant in Haddy- Littlewood- Sobolev inequality. In the case of initial free energy less than a universal constant which depends on the inverse of total mass, there exists a constant such that if the $L^{2n/(n+2)}$ norm of initial data is less than this constant, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0150","kind":"arxiv","version":2},"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":"1311.0150","created_at":"2026-05-18T03:05:57.352854+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.0150v2","created_at":"2026-05-18T03:05:57.352854+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0150","created_at":"2026-05-18T03:05:57.352854+00:00"},{"alias_kind":"pith_short_12","alias_value":"VICMN4WW2KCJ","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"VICMN4WW2KCJ5C62","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"VICMN4WW","created_at":"2026-05-18T12:28:04.890932+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/VICMN4WW2KCJ5C62JAIAVVSHMP","json":"https://pith.science/pith/VICMN4WW2KCJ5C62JAIAVVSHMP.json","graph_json":"https://pith.science/api/pith-number/VICMN4WW2KCJ5C62JAIAVVSHMP/graph.json","events_json":"https://pith.science/api/pith-number/VICMN4WW2KCJ5C62JAIAVVSHMP/events.json","paper":"https://pith.science/paper/VICMN4WW"},"agent_actions":{"view_html":"https://pith.science/pith/VICMN4WW2KCJ5C62JAIAVVSHMP","download_json":"https://pith.science/pith/VICMN4WW2KCJ5C62JAIAVVSHMP.json","view_paper":"https://pith.science/paper/VICMN4WW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.0150&json=true","fetch_graph":"https://pith.science/api/pith-number/VICMN4WW2KCJ5C62JAIAVVSHMP/graph.json","fetch_events":"https://pith.science/api/pith-number/VICMN4WW2KCJ5C62JAIAVVSHMP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VICMN4WW2KCJ5C62JAIAVVSHMP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VICMN4WW2KCJ5C62JAIAVVSHMP/action/storage_attestation","attest_author":"https://pith.science/pith/VICMN4WW2KCJ5C62JAIAVVSHMP/action/author_attestation","sign_citation":"https://pith.science/pith/VICMN4WW2KCJ5C62JAIAVVSHMP/action/citation_signature","submit_replication":"https://pith.science/pith/VICMN4WW2KCJ5C62JAIAVVSHMP/action/replication_record"}},"created_at":"2026-05-18T03:05:57.352854+00:00","updated_at":"2026-05-18T03:05:57.352854+00:00"}