{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5POJSKUNJIATRAF33DJYJQ4A6Y","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":"60580c03e49278935af89c408b41a7621a8562bdf97a3b7f158d4434f14f2f8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-19T16:21:01Z","title_canon_sha256":"3b9ec39b5c0882f07ba98656559bcda48a52ee758b6216211db0e5460d950747"},"schema_version":"1.0","source":{"id":"1506.06076","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06076","created_at":"2026-05-18T00:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06076v1","created_at":"2026-05-18T00:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06076","created_at":"2026-05-18T00:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"5POJSKUNJIAT","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5POJSKUNJIATRAF3","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5POJSKUN","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:dd4f50aac4c2ce0b6f57e518240a6bf8a76a1c3803d004ad6a931c25e84cba42","target":"graph","created_at":"2026-05-18T00:39:07Z","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 consider a parabolic-elliptic Keller-Segel type system, which is related to a simplified model of chemotaxis. Concerning the maximal range of existence of solutions, there are essentially two kinds of results: either global existence in time for general subcritical ($\\|\\rho_0\\|_1<8\\pi$) initial data, or blow--up in finite time for suitably chosen supercritical ($\\|\\rho_0\\|_1>8\\pi$) initial data with concentration around finitely many points. As a matter of fact there are no results claiming the existence of global solutions in the supercritical case. We solve this problem here and prove tha","authors_text":"Daniele Bartolucci, Daniele Castorina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-19T16:21:01Z","title":"A global existence result for a Keller-Segel type system with supercritical initial data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06076","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":"sha256:9998b3ba33382e5117520cdf67fd3f6f8fa0a26579ade8b7e4f1057fb5af7bf1","target":"record","created_at":"2026-05-18T00:39:07Z","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":"60580c03e49278935af89c408b41a7621a8562bdf97a3b7f158d4434f14f2f8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-19T16:21:01Z","title_canon_sha256":"3b9ec39b5c0882f07ba98656559bcda48a52ee758b6216211db0e5460d950747"},"schema_version":"1.0","source":{"id":"1506.06076","kind":"arxiv","version":1}},"canonical_sha256":"ebdc992a8d4a013880bbd8d384c380f61ae706ff2ef28a8b5b3734131ce6f0be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebdc992a8d4a013880bbd8d384c380f61ae706ff2ef28a8b5b3734131ce6f0be","first_computed_at":"2026-05-18T00:39:07.291599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:07.291599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j9qU60UGGt6Jrh8rFs4eNLqnGhj3tvwZnO2pk8+AlHDMomeMyhVe8YEdZvMCSYk3ZWgRrFPCfAF71qgP8SxuBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:07.292208Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06076","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9998b3ba33382e5117520cdf67fd3f6f8fa0a26579ade8b7e4f1057fb5af7bf1","sha256:dd4f50aac4c2ce0b6f57e518240a6bf8a76a1c3803d004ad6a931c25e84cba42"],"state_sha256":"9c326ea00878533d6daf54ba67e25a07d635dd5cd35d138ac0280b7e40d47b63"}