{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:UUSKDRTF2NNRVNQFJZ4UFOHJUT","short_pith_number":"pith:UUSKDRTF","schema_version":"1.0","canonical_sha256":"a524a1c665d35b1ab6054e7942b8e9a4c8cc64f4592a0a8a17dc7c920723566b","source":{"kind":"arxiv","id":"1401.7650","version":1},"attestation_state":"computed","paper":{"title":"Large global-in-time solutions of the parabolic-parabolic Keller-Segel system on the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Grzegorz Karch, Ignacio Guerra, Piotr Biler","submitted_at":"2014-01-29T20:29:48Z","abstract_excerpt":"As it is well known, the parabolic-elliptic Keller-Segel system of chemotaxis on the plane has global-in-time regular nonnegative solutions with total mass below the critical value $8\\pi$. Solutions with mass above $8\\pi$ blow up in a finite time. We show that the case of the parabolic-parabolic Keller-Segel is different: each mass may lead to a global-in-time-solution, even if the initial data is a finite signed measure.\n  These solutions need not be unique, even if we limit ourselves to nonnegative solutions."},"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":"1401.7650","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-29T20:29:48Z","cross_cats_sorted":[],"title_canon_sha256":"058152f5133090c71a043e8cdf4e39862b2b33b035b1cf5250ac70df30b84d06","abstract_canon_sha256":"1a368e4ddb7380476717f72ae228b2a66da6bb9805d0b82fe8467b72a118a45e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:40.246559Z","signature_b64":"XvDwz9ZvybRg55et4o9CCzl2BrfrtLAZCwMOad9jea6Qp/DAcsQziRZZjhLgUp5hNtMXHKdc/8Kp50xNmlkKBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a524a1c665d35b1ab6054e7942b8e9a4c8cc64f4592a0a8a17dc7c920723566b","last_reissued_at":"2026-05-18T03:00:40.245775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:40.245775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large global-in-time solutions of the parabolic-parabolic Keller-Segel system on the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Grzegorz Karch, Ignacio Guerra, Piotr Biler","submitted_at":"2014-01-29T20:29:48Z","abstract_excerpt":"As it is well known, the parabolic-elliptic Keller-Segel system of chemotaxis on the plane has global-in-time regular nonnegative solutions with total mass below the critical value $8\\pi$. Solutions with mass above $8\\pi$ blow up in a finite time. We show that the case of the parabolic-parabolic Keller-Segel is different: each mass may lead to a global-in-time-solution, even if the initial data is a finite signed measure.\n  These solutions need not be unique, even if we limit ourselves to nonnegative solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7650","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":"1401.7650","created_at":"2026-05-18T03:00:40.245894+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.7650v1","created_at":"2026-05-18T03:00:40.245894+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7650","created_at":"2026-05-18T03:00:40.245894+00:00"},{"alias_kind":"pith_short_12","alias_value":"UUSKDRTF2NNR","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"UUSKDRTF2NNRVNQF","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"UUSKDRTF","created_at":"2026-05-18T12:28:52.271510+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/UUSKDRTF2NNRVNQFJZ4UFOHJUT","json":"https://pith.science/pith/UUSKDRTF2NNRVNQFJZ4UFOHJUT.json","graph_json":"https://pith.science/api/pith-number/UUSKDRTF2NNRVNQFJZ4UFOHJUT/graph.json","events_json":"https://pith.science/api/pith-number/UUSKDRTF2NNRVNQFJZ4UFOHJUT/events.json","paper":"https://pith.science/paper/UUSKDRTF"},"agent_actions":{"view_html":"https://pith.science/pith/UUSKDRTF2NNRVNQFJZ4UFOHJUT","download_json":"https://pith.science/pith/UUSKDRTF2NNRVNQFJZ4UFOHJUT.json","view_paper":"https://pith.science/paper/UUSKDRTF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.7650&json=true","fetch_graph":"https://pith.science/api/pith-number/UUSKDRTF2NNRVNQFJZ4UFOHJUT/graph.json","fetch_events":"https://pith.science/api/pith-number/UUSKDRTF2NNRVNQFJZ4UFOHJUT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UUSKDRTF2NNRVNQFJZ4UFOHJUT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UUSKDRTF2NNRVNQFJZ4UFOHJUT/action/storage_attestation","attest_author":"https://pith.science/pith/UUSKDRTF2NNRVNQFJZ4UFOHJUT/action/author_attestation","sign_citation":"https://pith.science/pith/UUSKDRTF2NNRVNQFJZ4UFOHJUT/action/citation_signature","submit_replication":"https://pith.science/pith/UUSKDRTF2NNRVNQFJZ4UFOHJUT/action/replication_record"}},"created_at":"2026-05-18T03:00:40.245894+00:00","updated_at":"2026-05-18T03:00:40.245894+00:00"}