{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:M2GX2SVKLZQGNVTJJJOGHN74JR","short_pith_number":"pith:M2GX2SVK","schema_version":"1.0","canonical_sha256":"668d7d4aaa5e6066d6694a5c63b7fc4c7baba1644edd6ae53f37b2a499580c5d","source":{"kind":"arxiv","id":"1704.00667","version":1},"attestation_state":"computed","paper":{"title":"Dahlberg's theorem in higher co-dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guy David, Joseph Feneuil, Svitlana Mayboroda","submitted_at":"2017-04-03T16:27:30Z","abstract_excerpt":"In 1977 the celebrated theorem of B. Dahlberg established that the harmonic measure is absolutely continuous with respect to the Hausdorff measure on a Lipschitz graph of dimension $n-1$ in $\\mathbb R^n$, and later this result has been extended to more general non-tangentially accessible domains and beyond.\n  In the present paper we prove the first analogue of Dahlberg's theorem in higher co-dimension, on a Lipschitz graph $\\Gamma$ of dimension $d$ in $\\mathbb R^n$, $d<n-1$, with a small Lipschitz constant. We construct a linear degenerate elliptic operator $L$ such that the corresponding harm"},"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":"1704.00667","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-03T16:27:30Z","cross_cats_sorted":[],"title_canon_sha256":"6dff3acf9d6573732fbfbb2a0e16c633069874756d3d8d2592ec8d67e84930ff","abstract_canon_sha256":"a645bc3415bb7ad943e121fc0f355791eb76691b73274479ebf6b48ebde90820"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:21.671809Z","signature_b64":"xbGJE6zSOghHewR2UGjO5Cy8SkuobVQkIqXxejjJbyxMdrLBaS+4eUvQugq/czw+m108HDAciT57RHxdnbTXBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"668d7d4aaa5e6066d6694a5c63b7fc4c7baba1644edd6ae53f37b2a499580c5d","last_reissued_at":"2026-05-18T00:47:21.671187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:21.671187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dahlberg's theorem in higher co-dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guy David, Joseph Feneuil, Svitlana Mayboroda","submitted_at":"2017-04-03T16:27:30Z","abstract_excerpt":"In 1977 the celebrated theorem of B. Dahlberg established that the harmonic measure is absolutely continuous with respect to the Hausdorff measure on a Lipschitz graph of dimension $n-1$ in $\\mathbb R^n$, and later this result has been extended to more general non-tangentially accessible domains and beyond.\n  In the present paper we prove the first analogue of Dahlberg's theorem in higher co-dimension, on a Lipschitz graph $\\Gamma$ of dimension $d$ in $\\mathbb R^n$, $d<n-1$, with a small Lipschitz constant. We construct a linear degenerate elliptic operator $L$ such that the corresponding harm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00667","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":"1704.00667","created_at":"2026-05-18T00:47:21.671287+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.00667v1","created_at":"2026-05-18T00:47:21.671287+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00667","created_at":"2026-05-18T00:47:21.671287+00:00"},{"alias_kind":"pith_short_12","alias_value":"M2GX2SVKLZQG","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"M2GX2SVKLZQGNVTJ","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"M2GX2SVK","created_at":"2026-05-18T12:31:28.150371+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/M2GX2SVKLZQGNVTJJJOGHN74JR","json":"https://pith.science/pith/M2GX2SVKLZQGNVTJJJOGHN74JR.json","graph_json":"https://pith.science/api/pith-number/M2GX2SVKLZQGNVTJJJOGHN74JR/graph.json","events_json":"https://pith.science/api/pith-number/M2GX2SVKLZQGNVTJJJOGHN74JR/events.json","paper":"https://pith.science/paper/M2GX2SVK"},"agent_actions":{"view_html":"https://pith.science/pith/M2GX2SVKLZQGNVTJJJOGHN74JR","download_json":"https://pith.science/pith/M2GX2SVKLZQGNVTJJJOGHN74JR.json","view_paper":"https://pith.science/paper/M2GX2SVK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.00667&json=true","fetch_graph":"https://pith.science/api/pith-number/M2GX2SVKLZQGNVTJJJOGHN74JR/graph.json","fetch_events":"https://pith.science/api/pith-number/M2GX2SVKLZQGNVTJJJOGHN74JR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M2GX2SVKLZQGNVTJJJOGHN74JR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M2GX2SVKLZQGNVTJJJOGHN74JR/action/storage_attestation","attest_author":"https://pith.science/pith/M2GX2SVKLZQGNVTJJJOGHN74JR/action/author_attestation","sign_citation":"https://pith.science/pith/M2GX2SVKLZQGNVTJJJOGHN74JR/action/citation_signature","submit_replication":"https://pith.science/pith/M2GX2SVKLZQGNVTJJJOGHN74JR/action/replication_record"}},"created_at":"2026-05-18T00:47:21.671287+00:00","updated_at":"2026-05-18T00:47:21.671287+00:00"}