{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:M2GX2SVKLZQGNVTJJJOGHN74JR","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":"a645bc3415bb7ad943e121fc0f355791eb76691b73274479ebf6b48ebde90820","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-03T16:27:30Z","title_canon_sha256":"6dff3acf9d6573732fbfbb2a0e16c633069874756d3d8d2592ec8d67e84930ff"},"schema_version":"1.0","source":{"id":"1704.00667","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.00667","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"arxiv_version","alias_value":"1704.00667v1","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00667","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"pith_short_12","alias_value":"M2GX2SVKLZQG","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"M2GX2SVKLZQGNVTJ","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"M2GX2SVK","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:bed1ffdf09c386664ba8bc63e450889d20f13489aaac56344b7fa0a06753724a","target":"graph","created_at":"2026-05-18T00:47:21Z","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"},"paper":{"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","authors_text":"Guy David, Joseph Feneuil, Svitlana Mayboroda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-03T16:27:30Z","title":"Dahlberg's theorem in higher co-dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00667","kind":"arxiv","version":1},"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":"sha256:41ccf1dbdd237ab4c97e1874dac4037a702b0ca255b5e1333a6486c099a8c0a9","target":"record","created_at":"2026-05-18T00:47:21Z","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":"a645bc3415bb7ad943e121fc0f355791eb76691b73274479ebf6b48ebde90820","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-03T16:27:30Z","title_canon_sha256":"6dff3acf9d6573732fbfbb2a0e16c633069874756d3d8d2592ec8d67e84930ff"},"schema_version":"1.0","source":{"id":"1704.00667","kind":"arxiv","version":1}},"canonical_sha256":"668d7d4aaa5e6066d6694a5c63b7fc4c7baba1644edd6ae53f37b2a499580c5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"668d7d4aaa5e6066d6694a5c63b7fc4c7baba1644edd6ae53f37b2a499580c5d","first_computed_at":"2026-05-18T00:47:21.671187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:21.671187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xbGJE6zSOghHewR2UGjO5Cy8SkuobVQkIqXxejjJbyxMdrLBaS+4eUvQugq/czw+m108HDAciT57RHxdnbTXBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:21.671809Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.00667","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41ccf1dbdd237ab4c97e1874dac4037a702b0ca255b5e1333a6486c099a8c0a9","sha256:bed1ffdf09c386664ba8bc63e450889d20f13489aaac56344b7fa0a06753724a"],"state_sha256":"a2b043446a78d86e7f1c0a491f5fee47ba2f137b1532c9f47e01a2a0eedd3a18"}