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In particular, despite the term u M(x)∇ψ not being regular enough (since it only belongs to L²(Ω_T)), the solution u belongs to L^s(Ω_T)∩L^q(0,T;W^{1,q}_0(Ω)) for suitable s>1 and q>1.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The coefficients A(x,t) and M(x) satisfy the standard measurability, boundedness and uniform ellipticity conditions required to invoke the cited parabolic regularity theorems; these assumptions are implicit in the abstract but not stated explicitly.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Existence and higher summability are shown for solutions of a parabolic-elliptic system with discontinuous coefficients, L^1 data, and |u|^θ nonlinearity where θ < 2/N.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Existence of solutions to the parabolic-elliptic system is established for L1 data, with u gaining summability in L^s and L^q W^{1,q} despite the coupling term being only L2.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"258d98225c0c6f9a04650f11507f71568bf65e9fd87e31730667d23993191f64"},"source":{"id":"2604.16100","kind":"arxiv","version":2},"verdict":{"id":"334f3eaa-74d9-4bab-b8c2-f9359e9c7f0f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T08:12:21.821341Z","strongest_claim":"We prove existence results for data f∈L¹(Ω_T) and a corresponding increase in summability that obeys the L^p-regularity theorems for parabolic equations proved by Aronson-Serrin and by Boccardo-Dall'Aglio-Gallouët-Orsina. In particular, despite the term u M(x)∇ψ not being regular enough (since it only belongs to L²(Ω_T)), the solution u belongs to L^s(Ω_T)∩L^q(0,T;W^{1,q}_0(Ω)) for suitable s>1 and q>1.","one_line_summary":"Existence and higher summability are shown for solutions of a parabolic-elliptic system with discontinuous coefficients, L^1 data, and |u|^θ nonlinearity where θ < 2/N.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The coefficients A(x,t) and M(x) satisfy the standard measurability, boundedness and uniform ellipticity conditions required to invoke the cited parabolic regularity theorems; these assumptions are implicit in the abstract but not stated explicitly.","pith_extraction_headline":"Existence of solutions to the parabolic-elliptic system is established for L1 data, with u gaining summability in L^s and L^q W^{1,q} despite the coupling term being only L2."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.16100/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":"2604.16100","created_at":"2026-05-22T01:03:19.325100+00:00"},{"alias_kind":"arxiv_version","alias_value":"2604.16100v2","created_at":"2026-05-22T01:03:19.325100+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.16100","created_at":"2026-05-22T01:03:19.325100+00:00"},{"alias_kind":"pith_short_12","alias_value":"CNNFGHD3I5Z4","created_at":"2026-05-22T01:03:19.325100+00:00"},{"alias_kind":"pith_short_16","alias_value":"CNNFGHD3I5Z4IHHI","created_at":"2026-05-22T01:03:19.325100+00:00"},{"alias_kind":"pith_short_8","alias_value":"CNNFGHD3","created_at":"2026-05-22T01:03:19.325100+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/CNNFGHD3I5Z4IHHIB5WLHZZK2V","json":"https://pith.science/pith/CNNFGHD3I5Z4IHHIB5WLHZZK2V.json","graph_json":"https://pith.science/api/pith-number/CNNFGHD3I5Z4IHHIB5WLHZZK2V/graph.json","events_json":"https://pith.science/api/pith-number/CNNFGHD3I5Z4IHHIB5WLHZZK2V/events.json","paper":"https://pith.science/paper/CNNFGHD3"},"agent_actions":{"view_html":"https://pith.science/pith/CNNFGHD3I5Z4IHHIB5WLHZZK2V","download_json":"https://pith.science/pith/CNNFGHD3I5Z4IHHIB5WLHZZK2V.json","view_paper":"https://pith.science/paper/CNNFGHD3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2604.16100&json=true","fetch_graph":"https://pith.science/api/pith-number/CNNFGHD3I5Z4IHHIB5WLHZZK2V/graph.json","fetch_events":"https://pith.science/api/pith-number/CNNFGHD3I5Z4IHHIB5WLHZZK2V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CNNFGHD3I5Z4IHHIB5WLHZZK2V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CNNFGHD3I5Z4IHHIB5WLHZZK2V/action/storage_attestation","attest_author":"https://pith.science/pith/CNNFGHD3I5Z4IHHIB5WLHZZK2V/action/author_attestation","sign_citation":"https://pith.science/pith/CNNFGHD3I5Z4IHHIB5WLHZZK2V/action/citation_signature","submit_replication":"https://pith.science/pith/CNNFGHD3I5Z4IHHIB5WLHZZK2V/action/replication_record"}},"created_at":"2026-05-22T01:03:19.325100+00:00","updated_at":"2026-05-22T01:03:19.325100+00:00"}