{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UF7PA26BTJUP5TWNTOSDBMYIW5","short_pith_number":"pith:UF7PA26B","schema_version":"1.0","canonical_sha256":"a17ef06bc19a68fececd9ba430b308b75383db4e83df0240f426c0b121b99029","source":{"kind":"arxiv","id":"1511.09270","version":1},"attestation_state":"computed","paper":{"title":"The weak-$A_\\infty$ property of harmonic and $p$-harmonic measures implies uniform rectifiability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Jos\\'e Mar\\'ia Martell, Kaj Nystr\\\"om, Phi Le, Steve Hofmann","submitted_at":"2015-11-30T12:35:24Z","abstract_excerpt":"Let $E\\subset \\mathbb{R}^{n+1}$, $n\\ge 2$, be an Ahlfors-David regular set of dimension $n$. We show that the weak-$A_\\infty$ property of harmonic measure, for the open set $\\Omega:= \\mathbb{R}^{n+1}\\setminus E$, implies uniform rectifiability of $E$. More generally, we establish a similar result for the Riesz measure, $p$-harmonic measure, associated to the $p$-Laplace operator, $1<p<\\infty$."},"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":"1511.09270","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-11-30T12:35:24Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"50d1a247c6cafd52bdd55bc2afcd783d05006e11c4bd6468dc1ec414af6dbbfd","abstract_canon_sha256":"651d23f5ea8cf76d4d515f8d510a39e36234a67db9844028da3909adeb8c0f9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:50.592465Z","signature_b64":"+UrDgbtd6ZVZGPB7kH8pFD2ARp70jtlHC2iCYey98NJ9+ePAKvlPn/ImWA3xytvFXsg/9XWQrKy8yUE66H8sCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a17ef06bc19a68fececd9ba430b308b75383db4e83df0240f426c0b121b99029","last_reissued_at":"2026-05-18T00:03:50.591752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:50.591752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The weak-$A_\\infty$ property of harmonic and $p$-harmonic measures implies uniform rectifiability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Jos\\'e Mar\\'ia Martell, Kaj Nystr\\\"om, Phi Le, Steve Hofmann","submitted_at":"2015-11-30T12:35:24Z","abstract_excerpt":"Let $E\\subset \\mathbb{R}^{n+1}$, $n\\ge 2$, be an Ahlfors-David regular set of dimension $n$. We show that the weak-$A_\\infty$ property of harmonic measure, for the open set $\\Omega:= \\mathbb{R}^{n+1}\\setminus E$, implies uniform rectifiability of $E$. More generally, we establish a similar result for the Riesz measure, $p$-harmonic measure, associated to the $p$-Laplace operator, $1<p<\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09270","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":"1511.09270","created_at":"2026-05-18T00:03:50.591883+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.09270v1","created_at":"2026-05-18T00:03:50.591883+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09270","created_at":"2026-05-18T00:03:50.591883+00:00"},{"alias_kind":"pith_short_12","alias_value":"UF7PA26BTJUP","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UF7PA26BTJUP5TWN","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UF7PA26B","created_at":"2026-05-18T12:29:44.643036+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/UF7PA26BTJUP5TWNTOSDBMYIW5","json":"https://pith.science/pith/UF7PA26BTJUP5TWNTOSDBMYIW5.json","graph_json":"https://pith.science/api/pith-number/UF7PA26BTJUP5TWNTOSDBMYIW5/graph.json","events_json":"https://pith.science/api/pith-number/UF7PA26BTJUP5TWNTOSDBMYIW5/events.json","paper":"https://pith.science/paper/UF7PA26B"},"agent_actions":{"view_html":"https://pith.science/pith/UF7PA26BTJUP5TWNTOSDBMYIW5","download_json":"https://pith.science/pith/UF7PA26BTJUP5TWNTOSDBMYIW5.json","view_paper":"https://pith.science/paper/UF7PA26B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.09270&json=true","fetch_graph":"https://pith.science/api/pith-number/UF7PA26BTJUP5TWNTOSDBMYIW5/graph.json","fetch_events":"https://pith.science/api/pith-number/UF7PA26BTJUP5TWNTOSDBMYIW5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UF7PA26BTJUP5TWNTOSDBMYIW5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UF7PA26BTJUP5TWNTOSDBMYIW5/action/storage_attestation","attest_author":"https://pith.science/pith/UF7PA26BTJUP5TWNTOSDBMYIW5/action/author_attestation","sign_citation":"https://pith.science/pith/UF7PA26BTJUP5TWNTOSDBMYIW5/action/citation_signature","submit_replication":"https://pith.science/pith/UF7PA26BTJUP5TWNTOSDBMYIW5/action/replication_record"}},"created_at":"2026-05-18T00:03:50.591883+00:00","updated_at":"2026-05-18T00:03:50.591883+00:00"}