{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:ZK545GVBVHHQW3WWQD6A4HOEXP","short_pith_number":"pith:ZK545GVB","schema_version":"1.0","canonical_sha256":"cabbce9aa1a9cf0b6ed680fc0e1dc4bbe8a3d57a5f83430c170f630120e211ef","source":{"kind":"arxiv","id":"2311.00614","version":7},"attestation_state":"computed","paper":{"title":"Solvability of the Dirichlet problem for a new class of elliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Martin Ulmer","submitted_at":"2023-11-01T16:05:05Z","abstract_excerpt":"We study an elliptic operator $L:=\\mathrm{div}(A\\nabla \\cdot)$ on the upper half space. It is known that if the matrix $A$ is independent in the transversal $t$-direction, then we have $\\omega\\in A_\\infty(\\sigma)$. In the present paper we improve on the $t$-independence condition by introducing a mixed $L^1-L^\\infty$ Carleson type condition that only depends on $\\partial_t A$ and show $\\omega\\in A_\\infty(\\sigma)$ under this condition. This condition is different from other conditions in the literature.\n  In the case of the upper half plane, we obtain the improvement that an $L^1$-Carleson cond"},"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":"2311.00614","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-11-01T16:05:05Z","cross_cats_sorted":[],"title_canon_sha256":"55a85ccdb4e137052a2cac71bff2dad8e29921ba82d89802c5c071166260a62d","abstract_canon_sha256":"3e4df433da30269abff31a673451b28fe9493eef1b7c3469fdc8352be4c34173"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:47:10.478962Z","signature_b64":"AWpjXVulU6pnBym8lf0XjU6GzFX23/qtRHY4JIJBnkCf/LfFQbD9Uf0jdvorXJYIrsW5chsV3sQZnKiOT58TAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cabbce9aa1a9cf0b6ed680fc0e1dc4bbe8a3d57a5f83430c170f630120e211ef","last_reissued_at":"2026-07-05T11:47:10.478458Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:47:10.478458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solvability of the Dirichlet problem for a new class of elliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Martin Ulmer","submitted_at":"2023-11-01T16:05:05Z","abstract_excerpt":"We study an elliptic operator $L:=\\mathrm{div}(A\\nabla \\cdot)$ on the upper half space. It is known that if the matrix $A$ is independent in the transversal $t$-direction, then we have $\\omega\\in A_\\infty(\\sigma)$. In the present paper we improve on the $t$-independence condition by introducing a mixed $L^1-L^\\infty$ Carleson type condition that only depends on $\\partial_t A$ and show $\\omega\\in A_\\infty(\\sigma)$ under this condition. This condition is different from other conditions in the literature.\n  In the case of the upper half plane, we obtain the improvement that an $L^1$-Carleson cond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.00614","kind":"arxiv","version":7},"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/2311.00614/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":"2311.00614","created_at":"2026-07-05T11:47:10.478522+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.00614v7","created_at":"2026-07-05T11:47:10.478522+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.00614","created_at":"2026-07-05T11:47:10.478522+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZK545GVBVHHQ","created_at":"2026-07-05T11:47:10.478522+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZK545GVBVHHQW3WW","created_at":"2026-07-05T11:47:10.478522+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZK545GVB","created_at":"2026-07-05T11:47:10.478522+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.09614","citing_title":"The $L^p$ Neumann problem for parabolic operators with coefficients satisfying small Carleson condition","ref_index":30,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZK545GVBVHHQW3WWQD6A4HOEXP","json":"https://pith.science/pith/ZK545GVBVHHQW3WWQD6A4HOEXP.json","graph_json":"https://pith.science/api/pith-number/ZK545GVBVHHQW3WWQD6A4HOEXP/graph.json","events_json":"https://pith.science/api/pith-number/ZK545GVBVHHQW3WWQD6A4HOEXP/events.json","paper":"https://pith.science/paper/ZK545GVB"},"agent_actions":{"view_html":"https://pith.science/pith/ZK545GVBVHHQW3WWQD6A4HOEXP","download_json":"https://pith.science/pith/ZK545GVBVHHQW3WWQD6A4HOEXP.json","view_paper":"https://pith.science/paper/ZK545GVB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.00614&json=true","fetch_graph":"https://pith.science/api/pith-number/ZK545GVBVHHQW3WWQD6A4HOEXP/graph.json","fetch_events":"https://pith.science/api/pith-number/ZK545GVBVHHQW3WWQD6A4HOEXP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZK545GVBVHHQW3WWQD6A4HOEXP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZK545GVBVHHQW3WWQD6A4HOEXP/action/storage_attestation","attest_author":"https://pith.science/pith/ZK545GVBVHHQW3WWQD6A4HOEXP/action/author_attestation","sign_citation":"https://pith.science/pith/ZK545GVBVHHQW3WWQD6A4HOEXP/action/citation_signature","submit_replication":"https://pith.science/pith/ZK545GVBVHHQW3WWQD6A4HOEXP/action/replication_record"}},"created_at":"2026-07-05T11:47:10.478522+00:00","updated_at":"2026-07-05T11:47:10.478522+00:00"}