{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:H5Y5DPZBDPV5ZTUKWZWBOW27JV","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":"f4391f320ac68a8a0ff18443eac0a1735373954dad0db6eadf399da086b5087f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-13T06:05:01Z","title_canon_sha256":"95687533bdb6e82dc9eda9c270cb55a4075311a8d5288bbf964b040e421363df"},"schema_version":"1.0","source":{"id":"2501.07073","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.07073","created_at":"2026-07-05T10:41:19Z"},{"alias_kind":"arxiv_version","alias_value":"2501.07073v2","created_at":"2026-07-05T10:41:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.07073","created_at":"2026-07-05T10:41:19Z"},{"alias_kind":"pith_short_12","alias_value":"H5Y5DPZBDPV5","created_at":"2026-07-05T10:41:19Z"},{"alias_kind":"pith_short_16","alias_value":"H5Y5DPZBDPV5ZTUK","created_at":"2026-07-05T10:41:19Z"},{"alias_kind":"pith_short_8","alias_value":"H5Y5DPZB","created_at":"2026-07-05T10:41:19Z"}],"graph_snapshots":[{"event_id":"sha256:b671371b4302e250da6511a2a6ae8a18a0d95bb0fd1a76b66b3d1a54256e054f","target":"graph","created_at":"2026-07-05T10:41:19Z","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/2501.07073/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In three dimensions, the parabolic-elliptic Keller-Segel system exhibits a rich variety of singularity formations. Notably, it admits an explicit self-similar blow-up solution whose radial stability, conjectured more than two decades ago in [Brenner-Constantin-Kadanoff-Schenkel-Venkataramani, 1999], was recently confirmed by [Glogi\\'c-Sch\\\"orkhuber, 2024]. This paper aims to extend the radial stability to the nonradial setting, building on the finite-codimensional stability analysis in our previous work [Li-Zhou, 2024]. The main input is the mode stability of the linearized operator, whose non","authors_text":"Tao Zhou, Zexing Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-13T06:05:01Z","title":"Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.07073","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:e2ca6879c50438c98206fd45630279957da9c1d67ec20a48a9a66c161e64c08e","target":"record","created_at":"2026-07-05T10:41:19Z","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":"f4391f320ac68a8a0ff18443eac0a1735373954dad0db6eadf399da086b5087f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-13T06:05:01Z","title_canon_sha256":"95687533bdb6e82dc9eda9c270cb55a4075311a8d5288bbf964b040e421363df"},"schema_version":"1.0","source":{"id":"2501.07073","kind":"arxiv","version":2}},"canonical_sha256":"3f71d1bf211bebdcce8ab66c175b5f4d7c87f4ea6f1a4ee30e76b50b6575f361","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f71d1bf211bebdcce8ab66c175b5f4d7c87f4ea6f1a4ee30e76b50b6575f361","first_computed_at":"2026-07-05T10:41:19.658718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:41:19.658718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sKvryzZpYdQShV6xQfw72uQ3JPrZhrM3pldKDy2vpwOj688lLcwNx/Asdt8mhh/gzyFVEdMuCz52zVzWNOwLDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:41:19.659289Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.07073","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2ca6879c50438c98206fd45630279957da9c1d67ec20a48a9a66c161e64c08e","sha256:b671371b4302e250da6511a2a6ae8a18a0d95bb0fd1a76b66b3d1a54256e054f"],"state_sha256":"5e8595dd03bb9280044d279aca10f212de3ff8cac21b625274de850a3931a3b7"}