{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:G6HKNNATPTBENVUBQQ6GZGPPRM","short_pith_number":"pith:G6HKNNAT","schema_version":"1.0","canonical_sha256":"378ea6b4137cc246d681843c6c99ef8b27d2d9619587957b283308c8c06d885a","source":{"kind":"arxiv","id":"1610.00456","version":1},"attestation_state":"computed","paper":{"title":"Stability of infinite time blow up for the Patlak Keller Segel system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nader Masmoudi, Tej-Eddine Ghoul","submitted_at":"2016-10-03T09:17:08Z","abstract_excerpt":"We consider the parabolic-elliptic Patlak-Keller-Segel (PKS) model of chemotactic aggregation in two space dimensions which describes the aggregation of bacteria under chemo-taxis. When the mass is equal to $8\\pi$ and the second moment is finite (the doubly critical case), we give a precise description of the dynamic as time goes to infinity and extract the limiting profile and speed. The proof shows that this dynamic is stable under perturbations."},"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":"1610.00456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-03T09:17:08Z","cross_cats_sorted":[],"title_canon_sha256":"2f014812ae2c8409f9d9533b2c48545c98e70a66cf895fe830f9f11ad8111877","abstract_canon_sha256":"88b656caf0322220ebe6250da3da6848e54ef5c78e7a9c4c56ca4981d6ff4097"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:25.493920Z","signature_b64":"UX4dvQN4/qGpOBZ914gt7yW9riwuGtRTAGbIcpkAVyWBSIr5kO7JQpd4m0ELaF6p6gQaUqMuunnzyDF+4NNuBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"378ea6b4137cc246d681843c6c99ef8b27d2d9619587957b283308c8c06d885a","last_reissued_at":"2026-05-18T01:03:25.493283Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:25.493283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of infinite time blow up for the Patlak Keller Segel system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nader Masmoudi, Tej-Eddine Ghoul","submitted_at":"2016-10-03T09:17:08Z","abstract_excerpt":"We consider the parabolic-elliptic Patlak-Keller-Segel (PKS) model of chemotactic aggregation in two space dimensions which describes the aggregation of bacteria under chemo-taxis. When the mass is equal to $8\\pi$ and the second moment is finite (the doubly critical case), we give a precise description of the dynamic as time goes to infinity and extract the limiting profile and speed. The proof shows that this dynamic is stable under perturbations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00456","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":"1610.00456","created_at":"2026-05-18T01:03:25.493390+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.00456v1","created_at":"2026-05-18T01:03:25.493390+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00456","created_at":"2026-05-18T01:03:25.493390+00:00"},{"alias_kind":"pith_short_12","alias_value":"G6HKNNATPTBE","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"G6HKNNATPTBENVUB","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"G6HKNNAT","created_at":"2026-05-18T12:30:15.759754+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/G6HKNNATPTBENVUBQQ6GZGPPRM","json":"https://pith.science/pith/G6HKNNATPTBENVUBQQ6GZGPPRM.json","graph_json":"https://pith.science/api/pith-number/G6HKNNATPTBENVUBQQ6GZGPPRM/graph.json","events_json":"https://pith.science/api/pith-number/G6HKNNATPTBENVUBQQ6GZGPPRM/events.json","paper":"https://pith.science/paper/G6HKNNAT"},"agent_actions":{"view_html":"https://pith.science/pith/G6HKNNATPTBENVUBQQ6GZGPPRM","download_json":"https://pith.science/pith/G6HKNNATPTBENVUBQQ6GZGPPRM.json","view_paper":"https://pith.science/paper/G6HKNNAT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.00456&json=true","fetch_graph":"https://pith.science/api/pith-number/G6HKNNATPTBENVUBQQ6GZGPPRM/graph.json","fetch_events":"https://pith.science/api/pith-number/G6HKNNATPTBENVUBQQ6GZGPPRM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G6HKNNATPTBENVUBQQ6GZGPPRM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G6HKNNATPTBENVUBQQ6GZGPPRM/action/storage_attestation","attest_author":"https://pith.science/pith/G6HKNNATPTBENVUBQQ6GZGPPRM/action/author_attestation","sign_citation":"https://pith.science/pith/G6HKNNATPTBENVUBQQ6GZGPPRM/action/citation_signature","submit_replication":"https://pith.science/pith/G6HKNNATPTBENVUBQQ6GZGPPRM/action/replication_record"}},"created_at":"2026-05-18T01:03:25.493390+00:00","updated_at":"2026-05-18T01:03:25.493390+00:00"}