{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:UJAWGC5AT2JXTH7O2D7IKPI752","short_pith_number":"pith:UJAWGC5A","schema_version":"1.0","canonical_sha256":"a241630ba09e93799feed0fe853d1feebd35ebe6a53dccfe3ac7688d66e1f499","source":{"kind":"arxiv","id":"2605.13592","version":1},"attestation_state":"computed","paper":{"title":"Spectral instability and non-uniqueness of mild solutions for the Keller-Segel system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The parabolic-elliptic Keller-Segel system is locally ill-posed in L^q(R^n) for n from 3 to 9 and q in the supercritical range [1, n/2).","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Eliseo Luongo, Umberto Pappalettera","submitted_at":"2026-05-13T14:26:28Z","abstract_excerpt":"We show that the Cauchy problem associated with the parabolic-elliptic Keller-Segel model is locally ill-posed in $L^q(\\mathbb{R}^n)$ for dimensions $n \\in \\{3,\\dots,9\\}$ and throughout the supercritical range $q\\in [1,\\frac{n}{2})$. The non-uniqueness is driven by an instability mechanism in self-similarity variables, in the spirit of the program proposed by Jia and \\v{S}ver\\'ak for the three-dimensional Navier-Stokes equations."},"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":true,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.13592","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-13T14:26:28Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"cc838549e3beda93ff314105ecf054f0e0215f3e390bee8f0f7b2d000b88d5fc","abstract_canon_sha256":"776a23c53d173fab09784b88b51961b5a9075544b82d22520770ccab660205a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:23.053952Z","signature_b64":"pkOb5n06YcyHVGGNnAdTSLuYr3vONhD6ysZjt8otAYN3E5aA/BHljZXUanyoHMT/j+mXXOYafj00gaD+anxJCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a241630ba09e93799feed0fe853d1feebd35ebe6a53dccfe3ac7688d66e1f499","last_reissued_at":"2026-05-18T02:44:23.053536Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:23.053536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral instability and non-uniqueness of mild solutions for the Keller-Segel system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The parabolic-elliptic Keller-Segel system is locally ill-posed in L^q(R^n) for n from 3 to 9 and q in the supercritical range [1, n/2).","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Eliseo Luongo, Umberto Pappalettera","submitted_at":"2026-05-13T14:26:28Z","abstract_excerpt":"We show that the Cauchy problem associated with the parabolic-elliptic Keller-Segel model is locally ill-posed in $L^q(\\mathbb{R}^n)$ for dimensions $n \\in \\{3,\\dots,9\\}$ and throughout the supercritical range $q\\in [1,\\frac{n}{2})$. The non-uniqueness is driven by an instability mechanism in self-similarity variables, in the spirit of the program proposed by Jia and \\v{S}ver\\'ak for the three-dimensional Navier-Stokes equations."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that the Cauchy problem associated with the parabolic-elliptic Keller-Segel model is locally ill-posed in L^q(R^n) for dimensions n ∈ {3,…,9} and throughout the supercritical range q∈[1,n/2).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The non-uniqueness is driven by an instability mechanism in self-similarity variables, assuming the spectral instability from the Jia-Šverák Navier-Stokes program transfers directly to the Keller-Segel linearization without extra obstructions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The parabolic-elliptic Keller-Segel system is locally ill-posed in L^q(R^n) for n=3..9 and supercritical q in [1, n/2).","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The parabolic-elliptic Keller-Segel system is locally ill-posed in L^q(R^n) for n from 3 to 9 and q in the supercritical range [1, n/2).","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"31f7dda5ed02db7121927bf92f430ae961e8c356ce9955880a8ccb65fec597cf"},"source":{"id":"2605.13592","kind":"arxiv","version":1},"verdict":{"id":"8e263e9f-8146-46d9-bdf9-f6b35068d3c1","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:17:51.884951Z","strongest_claim":"We show that the Cauchy problem associated with the parabolic-elliptic Keller-Segel model is locally ill-posed in L^q(R^n) for dimensions n ∈ {3,…,9} and throughout the supercritical range q∈[1,n/2).","one_line_summary":"The parabolic-elliptic Keller-Segel system is locally ill-posed in L^q(R^n) for n=3..9 and supercritical q in [1, n/2).","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The non-uniqueness is driven by an instability mechanism in self-similarity variables, assuming the spectral instability from the Jia-Šverák Navier-Stokes program transfers directly to the Keller-Segel linearization without extra obstructions.","pith_extraction_headline":"The parabolic-elliptic Keller-Segel system is locally ill-posed in L^q(R^n) for n from 3 to 9 and q in the supercritical range [1, n/2)."},"references":{"count":46,"sample":[{"doi":"10.1007/s00205-016-1017-8","year":2016,"title":"Archive for Rational Mechanics and Analysis , VOLUME =","work_id":"fc647668-0c9d-416d-b3ec-d992c2243613","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/j.jfa.2024.110541","year":2024,"title":"Journal of Functional Analysis , VOLUME =","work_id":"1cd36c6c-66b5-4481-8957-9e9d8d92413a","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/s00039-025-00706-0","year":2025,"title":"Geometric and Functional Analysis , VOLUME =","work_id":"5bf8873e-b3b3-43ec-8b62-61b3ad6a39dc","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/s40818-023-00155-8","year":2023,"title":"Annals of PDE , VOLUME =","work_id":"bcc3018c-158e-4e77-a93a-26d4b239ade3","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1515/crelle-2025-0025","year":2025,"title":"Journal f\\\"ur die Reine und Angewandte Mathematik","work_id":"1d9eea7a-4107-495d-8311-f6ea82d671ad","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":46,"snapshot_sha256":"990b1dc87bfab577032c00e396740ebe2f4fa2869685f36c560591bd46be9c29","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":"2605.13592","created_at":"2026-05-18T02:44:23.053600+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.13592v1","created_at":"2026-05-18T02:44:23.053600+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13592","created_at":"2026-05-18T02:44:23.053600+00:00"},{"alias_kind":"pith_short_12","alias_value":"UJAWGC5AT2JX","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"UJAWGC5AT2JXTH7O","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"UJAWGC5A","created_at":"2026-05-18T12:33:37.589309+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/UJAWGC5AT2JXTH7O2D7IKPI752","json":"https://pith.science/pith/UJAWGC5AT2JXTH7O2D7IKPI752.json","graph_json":"https://pith.science/api/pith-number/UJAWGC5AT2JXTH7O2D7IKPI752/graph.json","events_json":"https://pith.science/api/pith-number/UJAWGC5AT2JXTH7O2D7IKPI752/events.json","paper":"https://pith.science/paper/UJAWGC5A"},"agent_actions":{"view_html":"https://pith.science/pith/UJAWGC5AT2JXTH7O2D7IKPI752","download_json":"https://pith.science/pith/UJAWGC5AT2JXTH7O2D7IKPI752.json","view_paper":"https://pith.science/paper/UJAWGC5A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.13592&json=true","fetch_graph":"https://pith.science/api/pith-number/UJAWGC5AT2JXTH7O2D7IKPI752/graph.json","fetch_events":"https://pith.science/api/pith-number/UJAWGC5AT2JXTH7O2D7IKPI752/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UJAWGC5AT2JXTH7O2D7IKPI752/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UJAWGC5AT2JXTH7O2D7IKPI752/action/storage_attestation","attest_author":"https://pith.science/pith/UJAWGC5AT2JXTH7O2D7IKPI752/action/author_attestation","sign_citation":"https://pith.science/pith/UJAWGC5AT2JXTH7O2D7IKPI752/action/citation_signature","submit_replication":"https://pith.science/pith/UJAWGC5AT2JXTH7O2D7IKPI752/action/replication_record"}},"created_at":"2026-05-18T02:44:23.053600+00:00","updated_at":"2026-05-18T02:44:23.053600+00:00"}