{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UQEGZJNAVSORMIEFLYADRC5KEH","short_pith_number":"pith:UQEGZJNA","schema_version":"1.0","canonical_sha256":"a4086ca5a0ac9d1620855e00388baa21c416d97603295ccd69d1a55bc3ae137b","source":{"kind":"arxiv","id":"1903.00124","version":1},"attestation_state":"computed","paper":{"title":"Extensibility criterion ruling out gradient blow-up in a quasilinear degenerate chemotaxis system with flux limitation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masaaki Mizukami, Tatsuhiko Ono, Tomomi Yokota","submitted_at":"2019-03-01T01:54:23Z","abstract_excerpt":"This paper deals with the quasilinear degenerate chemotaxis system with flux limitation \\begin{equation*} \\begin{cases} u_t = \\nabla\\cdot\\left(\\dfrac{u^p \\nabla u}{\\sqrt{u^2 + |\\nabla u|^2}} \\right) -\\chi \\nabla\\cdot\\left(\\dfrac{u^q\\nabla v}{\\sqrt{1 + |\\nabla v|^2}}\\right), \\\\[1mm] 0 = \\Delta v - \\mu + u \\end{cases}\\end{equation*} under no-flux boundary conditions in balls $\\Omega\\subset\\mathbb{R}^n$, and the initial condition $u|_{t=0}=u_0$ for a radially symmetric and positive initial data $u_0\\in C^3(\\overline{\\Omega})$, where $\\chi>0$ and $\\mu:=\\frac{1}{|\\Omega|}\\int_{\\Omega}u_0$. Bellomo-"},"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":"1903.00124","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-01T01:54:23Z","cross_cats_sorted":[],"title_canon_sha256":"b8c019a1c2c59ac1e211aed7b1075023bfd5122d1a7414949684a046ea0e436e","abstract_canon_sha256":"71f68b790a913f2e30e38b44c48d99c076581d515f0959968552ccbffb067424"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:22.959930Z","signature_b64":"w+K4q82O1GmLsaDAdsqiKEhu3HC/xQPW9vG/Ad8Gh2WX5WeFE2BtCy7V4ujzLBX/3yqexLUp+yDjpWbTVKKuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4086ca5a0ac9d1620855e00388baa21c416d97603295ccd69d1a55bc3ae137b","last_reissued_at":"2026-05-17T23:49:22.959464Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:22.959464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extensibility criterion ruling out gradient blow-up in a quasilinear degenerate chemotaxis system with flux limitation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masaaki Mizukami, Tatsuhiko Ono, Tomomi Yokota","submitted_at":"2019-03-01T01:54:23Z","abstract_excerpt":"This paper deals with the quasilinear degenerate chemotaxis system with flux limitation \\begin{equation*} \\begin{cases} u_t = \\nabla\\cdot\\left(\\dfrac{u^p \\nabla u}{\\sqrt{u^2 + |\\nabla u|^2}} \\right) -\\chi \\nabla\\cdot\\left(\\dfrac{u^q\\nabla v}{\\sqrt{1 + |\\nabla v|^2}}\\right), \\\\[1mm] 0 = \\Delta v - \\mu + u \\end{cases}\\end{equation*} under no-flux boundary conditions in balls $\\Omega\\subset\\mathbb{R}^n$, and the initial condition $u|_{t=0}=u_0$ for a radially symmetric and positive initial data $u_0\\in C^3(\\overline{\\Omega})$, where $\\chi>0$ and $\\mu:=\\frac{1}{|\\Omega|}\\int_{\\Omega}u_0$. Bellomo-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00124","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":"1903.00124","created_at":"2026-05-17T23:49:22.959532+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.00124v1","created_at":"2026-05-17T23:49:22.959532+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00124","created_at":"2026-05-17T23:49:22.959532+00:00"},{"alias_kind":"pith_short_12","alias_value":"UQEGZJNAVSOR","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"UQEGZJNAVSORMIEF","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"UQEGZJNA","created_at":"2026-05-18T12:33:30.264802+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/UQEGZJNAVSORMIEFLYADRC5KEH","json":"https://pith.science/pith/UQEGZJNAVSORMIEFLYADRC5KEH.json","graph_json":"https://pith.science/api/pith-number/UQEGZJNAVSORMIEFLYADRC5KEH/graph.json","events_json":"https://pith.science/api/pith-number/UQEGZJNAVSORMIEFLYADRC5KEH/events.json","paper":"https://pith.science/paper/UQEGZJNA"},"agent_actions":{"view_html":"https://pith.science/pith/UQEGZJNAVSORMIEFLYADRC5KEH","download_json":"https://pith.science/pith/UQEGZJNAVSORMIEFLYADRC5KEH.json","view_paper":"https://pith.science/paper/UQEGZJNA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.00124&json=true","fetch_graph":"https://pith.science/api/pith-number/UQEGZJNAVSORMIEFLYADRC5KEH/graph.json","fetch_events":"https://pith.science/api/pith-number/UQEGZJNAVSORMIEFLYADRC5KEH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UQEGZJNAVSORMIEFLYADRC5KEH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UQEGZJNAVSORMIEFLYADRC5KEH/action/storage_attestation","attest_author":"https://pith.science/pith/UQEGZJNAVSORMIEFLYADRC5KEH/action/author_attestation","sign_citation":"https://pith.science/pith/UQEGZJNAVSORMIEFLYADRC5KEH/action/citation_signature","submit_replication":"https://pith.science/pith/UQEGZJNAVSORMIEFLYADRC5KEH/action/replication_record"}},"created_at":"2026-05-17T23:49:22.959532+00:00","updated_at":"2026-05-17T23:49:22.959532+00:00"}