{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:OHO2SVKWAZQU4D534ZITWSY7YU","short_pith_number":"pith:OHO2SVKW","schema_version":"1.0","canonical_sha256":"71dda9555606614e0fbbe6513b4b1fc50ad63eaa7f59f86a036083900e4b724f","source":{"kind":"arxiv","id":"2507.19866","version":1},"attestation_state":"computed","paper":{"title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hengling Wang, Jianlu Yan, Xuan Mao","submitted_at":"2025-07-26T08:45:29Z","abstract_excerpt":"This paper investigates the flux-limited chemotaxis system, proposed by Kohatsu and Senba~(2025), \\begin{equation*}\n  \\begin{cases} u_t = \\Delta u -\\nabla\\cdot(u|\\nabla v|^{\\alpha-2}\\nabla v),\\\\ \\:\\:0=\\Delta v + u,\n  \\end{cases} \\end{equation*} posed in the unit ball of $\\mathbb{R}^N$ for some $N\\geq2$, subject to no-flux and homogeneous Dirichlet boundary conditions. Due to precedents, e.g., Tello (2022) and Winkler (2022), the exponent $\\alpha = \\frac{N}{N-1}$ is the threshold for finite-time blow-up under symmetry assumptions. We further find that under the framework of radially symmetric s"},"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":"2507.19866","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-07-26T08:45:29Z","cross_cats_sorted":[],"title_canon_sha256":"49e22d294c8b4dc392518015d3b13bb18bc5dd14402207de84a91ec63baa1d8d","abstract_canon_sha256":"0bf3276a0acd1a322fef4d6e7e72a5b27dc7d614b0cb87098e2b7fe86509bfb4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:43:43.911927Z","signature_b64":"Z+pihNplkHCO8JpeAnFDQZbB3Esnt1H7YYQhYZOb9/9FthjixrymdG2wraLdJZcAsKG5Q3Ogp38heFIBbR98DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71dda9555606614e0fbbe6513b4b1fc50ad63eaa7f59f86a036083900e4b724f","last_reissued_at":"2026-07-05T11:43:43.911456Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:43:43.911456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mass threshold for global existence in chemotaxis systems with critical flux limitation","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hengling Wang, Jianlu Yan, Xuan Mao","submitted_at":"2025-07-26T08:45:29Z","abstract_excerpt":"This paper investigates the flux-limited chemotaxis system, proposed by Kohatsu and Senba~(2025), \\begin{equation*}\n  \\begin{cases} u_t = \\Delta u -\\nabla\\cdot(u|\\nabla v|^{\\alpha-2}\\nabla v),\\\\ \\:\\:0=\\Delta v + u,\n  \\end{cases} \\end{equation*} posed in the unit ball of $\\mathbb{R}^N$ for some $N\\geq2$, subject to no-flux and homogeneous Dirichlet boundary conditions. Due to precedents, e.g., Tello (2022) and Winkler (2022), the exponent $\\alpha = \\frac{N}{N-1}$ is the threshold for finite-time blow-up under symmetry assumptions. We further find that under the framework of radially symmetric s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19866","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.19866/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2507.19866","created_at":"2026-07-05T11:43:43.911514+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.19866v1","created_at":"2026-07-05T11:43:43.911514+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.19866","created_at":"2026-07-05T11:43:43.911514+00:00"},{"alias_kind":"pith_short_12","alias_value":"OHO2SVKWAZQU","created_at":"2026-07-05T11:43:43.911514+00:00"},{"alias_kind":"pith_short_16","alias_value":"OHO2SVKWAZQU4D53","created_at":"2026-07-05T11:43:43.911514+00:00"},{"alias_kind":"pith_short_8","alias_value":"OHO2SVKW","created_at":"2026-07-05T11:43:43.911514+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/OHO2SVKWAZQU4D534ZITWSY7YU","json":"https://pith.science/pith/OHO2SVKWAZQU4D534ZITWSY7YU.json","graph_json":"https://pith.science/api/pith-number/OHO2SVKWAZQU4D534ZITWSY7YU/graph.json","events_json":"https://pith.science/api/pith-number/OHO2SVKWAZQU4D534ZITWSY7YU/events.json","paper":"https://pith.science/paper/OHO2SVKW"},"agent_actions":{"view_html":"https://pith.science/pith/OHO2SVKWAZQU4D534ZITWSY7YU","download_json":"https://pith.science/pith/OHO2SVKWAZQU4D534ZITWSY7YU.json","view_paper":"https://pith.science/paper/OHO2SVKW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.19866&json=true","fetch_graph":"https://pith.science/api/pith-number/OHO2SVKWAZQU4D534ZITWSY7YU/graph.json","fetch_events":"https://pith.science/api/pith-number/OHO2SVKWAZQU4D534ZITWSY7YU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OHO2SVKWAZQU4D534ZITWSY7YU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OHO2SVKWAZQU4D534ZITWSY7YU/action/storage_attestation","attest_author":"https://pith.science/pith/OHO2SVKWAZQU4D534ZITWSY7YU/action/author_attestation","sign_citation":"https://pith.science/pith/OHO2SVKWAZQU4D534ZITWSY7YU/action/citation_signature","submit_replication":"https://pith.science/pith/OHO2SVKWAZQU4D534ZITWSY7YU/action/replication_record"}},"created_at":"2026-07-05T11:43:43.911514+00:00","updated_at":"2026-07-05T11:43:43.911514+00:00"}