{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7BO6M46UG3PQJYELYTAFKZBPPZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1e4344979823a4014237b7719d78ff5bf2cb834a84233470fb806e73fca06f30","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-07-29T19:21:50Z","title_canon_sha256":"35974e4cb521e039a61b00eef6dbbfddbf491c6792ebd0c6457c2c949f0014ab"},"schema_version":"1.0","source":{"id":"2407.20385","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.20385","created_at":"2026-07-05T09:32:11Z"},{"alias_kind":"arxiv_version","alias_value":"2407.20385v3","created_at":"2026-07-05T09:32:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.20385","created_at":"2026-07-05T09:32:11Z"},{"alias_kind":"pith_short_12","alias_value":"7BO6M46UG3PQ","created_at":"2026-07-05T09:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7BO6M46UG3PQJYEL","created_at":"2026-07-05T09:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7BO6M46U","created_at":"2026-07-05T09:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:6e2e1d1841dd41cec8822c13795f112873a95a5f361170c4eb45c9a2059cc628","target":"graph","created_at":"2026-07-05T09:32:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2407.20385/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\Omega \\subset \\mathbb{R}^{n+1}$ be a bounded chord-arc domain, let $\\mathcal L=-{\\rm div} A\\nabla$ be an elliptic operator in $\\Omega$ associated with a matrix $A$ having Dini mean oscillation coefficients, and let $1<p\\leq 2$. In this paper we show that if the regularity problem for $\\mathcal L$ is solvable in $L^q$ for some $q>p$ in $\\Omega$, $\\partial \\Omega$ supports a weak $p$-Poincar\\'e inequality, and $\\Omega$ has very big pieces of superdomains for which the Neumann problem for $\\mathcal L$ is solvable uniformly in $L^q$, then the Neumann problem for $\\mathcal L$ is solvable in $","authors_text":"Mihalis Mourgoglou, Xavier Tolsa","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-07-29T19:21:50Z","title":"Solvability of the Neumann problem for elliptic equations in chord-arc domains with very big pieces of good superdomains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.20385","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:996a2ff34ddca1a1aecc3f3d3087b1d9f35fb6178b115de9cfcb891112d44235","target":"record","created_at":"2026-07-05T09:32:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1e4344979823a4014237b7719d78ff5bf2cb834a84233470fb806e73fca06f30","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-07-29T19:21:50Z","title_canon_sha256":"35974e4cb521e039a61b00eef6dbbfddbf491c6792ebd0c6457c2c949f0014ab"},"schema_version":"1.0","source":{"id":"2407.20385","kind":"arxiv","version":3}},"canonical_sha256":"f85de673d436df04e08bc4c055642f7e671d006093c2af617f74afdaed577e3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f85de673d436df04e08bc4c055642f7e671d006093c2af617f74afdaed577e3d","first_computed_at":"2026-07-05T09:32:11.201648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:32:11.201648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5sG/HrjxtX3QGXK05KwpotAVvX8hJ7jR884Y/DT6aLxxyf6zO0+GrpmNNM6FNTSWuAkjPQbV2d25HHpKmVEzAA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:32:11.202136Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.20385","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:996a2ff34ddca1a1aecc3f3d3087b1d9f35fb6178b115de9cfcb891112d44235","sha256:6e2e1d1841dd41cec8822c13795f112873a95a5f361170c4eb45c9a2059cc628"],"state_sha256":"c46fa8e0ad4f9a2098b7b4218e9dee3ba0eb7c976fae8e94026b635a3b4b63c8"}