{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DHOQBCZLUHZZVYJC4BJ2VNYREH","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":"cb09212bc65db39cf0e6acbeeaccb6c356f9295a50ce84b48bcf2eaae26e655f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-13T16:58:07Z","title_canon_sha256":"e0428c32b8177d75c9b245512de0896cb66ca075311aa000d41e0e1f759a8dab"},"schema_version":"1.0","source":{"id":"1609.03935","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03935","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03935v1","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03935","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"DHOQBCZLUHZZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DHOQBCZLUHZZVYJC","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DHOQBCZL","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:43ae8d5e950264e3590ae6091a0e84d0891bc226d3f21da434b00d15884d4bfb","target":"graph","created_at":"2026-05-18T01:04:42Z","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 two dimensional parabolic-elliptic Keller-Segel equation with a logistic forcing and a fractional diffusion of order $\\alpha$. We obtain existence of global in time regular solution for arbitrary initial data with no size restrictions and $c<\\alpha\\leq 2$, where $c \\in (0,2)$ depends on the equation's parameters. For an even wider range of $\\alpha's$, we prove existence of global in time weak solution for general initial data.","authors_text":"Jan Burczak, Rafael Granero-Belinch\\'on","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-13T16:58:07Z","title":"Suppression of blow up by a logistic source in $2$D Keller-Segel system with fractional dissipation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03935","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:af95d3d896e4ea7297016ba476fe2845215c3f3e62bbaf2623b71eafef007d09","target":"record","created_at":"2026-05-18T01:04:42Z","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":"cb09212bc65db39cf0e6acbeeaccb6c356f9295a50ce84b48bcf2eaae26e655f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-13T16:58:07Z","title_canon_sha256":"e0428c32b8177d75c9b245512de0896cb66ca075311aa000d41e0e1f759a8dab"},"schema_version":"1.0","source":{"id":"1609.03935","kind":"arxiv","version":1}},"canonical_sha256":"19dd008b2ba1f39ae122e053aab71121fb042c80dfcf058fe1ddc9a15376e7b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19dd008b2ba1f39ae122e053aab71121fb042c80dfcf058fe1ddc9a15376e7b7","first_computed_at":"2026-05-18T01:04:42.132859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:42.132859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9qYDXbu8QbVqoPFwIZorS/5lyWWrp1DazIUBop0tDqEDCblDJZZMdTr1xxBSQM87Mslj64tXzxObZaEUyeerBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:42.133333Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03935","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af95d3d896e4ea7297016ba476fe2845215c3f3e62bbaf2623b71eafef007d09","sha256:43ae8d5e950264e3590ae6091a0e84d0891bc226d3f21da434b00d15884d4bfb"],"state_sha256":"1298cc93a0b770f9ba7be768cf86540a264228e6c60be717d83fd1932141941f"}