{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:SCQJJVTY3MPKPBIIPXYMZDH2SW","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":"37d0f78f5be4f3d28ce3016832a6319db0b851004c87ff2d2d50b408a718f85a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-12-31T15:37:01Z","title_canon_sha256":"f68aa1ffaa2a40b89b87ab582101b223dba56a495bc3047f1c10e90e3aff2fb9"},"schema_version":"1.0","source":{"id":"2112.15518","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.15518","created_at":"2026-07-05T03:48:48Z"},{"alias_kind":"arxiv_version","alias_value":"2112.15518v2","created_at":"2026-07-05T03:48:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.15518","created_at":"2026-07-05T03:48:48Z"},{"alias_kind":"pith_short_12","alias_value":"SCQJJVTY3MPK","created_at":"2026-07-05T03:48:48Z"},{"alias_kind":"pith_short_16","alias_value":"SCQJJVTY3MPKPBII","created_at":"2026-07-05T03:48:48Z"},{"alias_kind":"pith_short_8","alias_value":"SCQJJVTY","created_at":"2026-07-05T03:48:48Z"}],"graph_snapshots":[{"event_id":"sha256:88e7e29430297e59683c483b7047fc969de700b2112867b84270680226c46419","target":"graph","created_at":"2026-07-05T03:48:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2112.15518/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the parabolic-elliptic Keller-Segel system in three dimensions and higher, corresponding to the mass supercritical case. We construct rigorously a solution which blows up in finite time by having its mass concentrating near a ring that shrinks to a point. In particular, the singularity is of type II, non self-similar. We show the stability of this dynamics among spherically symmetric solutions. In renormalised variables, the solution ressembles a traveling wave imploding at the origin, and this, to our knowledge, is the first stability result for such phenomenon for an evolution PD","authors_text":"Charles Collot, Nader Masmoudi, Tej-Eddine Ghoul, Van Tien Nguyen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-12-31T15:37:01Z","title":"Collapsing-ring blowup solutions for the Keller-Segel system in three dimensions and higher"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.15518","kind":"arxiv","version":2},"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:fead1f6efb0573d547410e023c96316aebacdfd4f96f1c36ff8b1e85eb8352fb","target":"record","created_at":"2026-07-05T03:48:48Z","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":"37d0f78f5be4f3d28ce3016832a6319db0b851004c87ff2d2d50b408a718f85a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-12-31T15:37:01Z","title_canon_sha256":"f68aa1ffaa2a40b89b87ab582101b223dba56a495bc3047f1c10e90e3aff2fb9"},"schema_version":"1.0","source":{"id":"2112.15518","kind":"arxiv","version":2}},"canonical_sha256":"90a094d678db1ea785087df0cc8cfa95b39e8785f80260e45f3dd00b00ff72a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90a094d678db1ea785087df0cc8cfa95b39e8785f80260e45f3dd00b00ff72a9","first_computed_at":"2026-07-05T03:48:48.576543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:48:48.576543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zoLC0DIOxQmhJgqV3ezseXQ0fVuZoJ7Ucre/di43dsuuu0h54yI6PdIKjDt1cYoj1PpRA0F08cUnlj/pCp7hCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:48:48.576885Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.15518","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fead1f6efb0573d547410e023c96316aebacdfd4f96f1c36ff8b1e85eb8352fb","sha256:88e7e29430297e59683c483b7047fc969de700b2112867b84270680226c46419"],"state_sha256":"72a5569d815c30805aee5bcfa29044fad3c39c70fbe7e76965d497f238f2abb4"}