{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:2ODIHZA2XDOU4GIYS6RUD32PDN","short_pith_number":"pith:2ODIHZA2","canonical_record":{"source":{"id":"1908.03161","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-08T16:40:29Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3ae45dfcc0f4ac4d97e26645ea9da07403977c18e205c3d8b2c1547022f37e0f","abstract_canon_sha256":"488dd3b98d378e6466be5c3f72555537c094ff9978dff905aaf9da3c8279ccbd"},"schema_version":"1.0"},"canonical_sha256":"d38683e41ab8dd4e191897a341ef4f1b7794e1ece01a60af4652d36eb93ccb76","source":{"kind":"arxiv","id":"1908.03161","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03161","created_at":"2026-07-05T00:30:20Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03161v2","created_at":"2026-07-05T00:30:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03161","created_at":"2026-07-05T00:30:20Z"},{"alias_kind":"pith_short_12","alias_value":"2ODIHZA2XDOU","created_at":"2026-07-05T00:30:20Z"},{"alias_kind":"pith_short_16","alias_value":"2ODIHZA2XDOU4GIY","created_at":"2026-07-05T00:30:20Z"},{"alias_kind":"pith_short_8","alias_value":"2ODIHZA2","created_at":"2026-07-05T00:30:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:2ODIHZA2XDOU4GIYS6RUD32PDN","target":"record","payload":{"canonical_record":{"source":{"id":"1908.03161","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-08T16:40:29Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3ae45dfcc0f4ac4d97e26645ea9da07403977c18e205c3d8b2c1547022f37e0f","abstract_canon_sha256":"488dd3b98d378e6466be5c3f72555537c094ff9978dff905aaf9da3c8279ccbd"},"schema_version":"1.0"},"canonical_sha256":"d38683e41ab8dd4e191897a341ef4f1b7794e1ece01a60af4652d36eb93ccb76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:30:20.402235Z","signature_b64":"bUoPA4X3UdL2LQ3Yg+OKWwf08XzhDsPkJBLRq1BRaTJOICBs1JVNU4yTDak6xDjGlujX/2PKsFpGaLRAVed1DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d38683e41ab8dd4e191897a341ef4f1b7794e1ece01a60af4652d36eb93ccb76","last_reissued_at":"2026-07-05T00:30:20.401830Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:30:20.401830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.03161","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:30:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hdM3OqNl7qC7WzQieWTHUJZ8N2hRBbxYW2uxuRuWnB/UvRsCkr7T/cvUzOPhOIFDUu8eECMtT9ti0QxJv1QXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:48:10.300718Z"},"content_sha256":"169d7e1e97d0136fb6af1a6818f3bf7320184eb7967bb1a35431f416ad8eb506","schema_version":"1.0","event_id":"sha256:169d7e1e97d0136fb6af1a6818f3bf7320184eb7967bb1a35431f416ad8eb506"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:2ODIHZA2XDOU4GIYS6RUD32PDN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform rectifiability and elliptic operators satisfying a Carleson measure condition. Part II: The large constant case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Jos\\'e Mar\\'ia Martell, Steve Hofmann, Svitlana Mayboroda, Tatiana Toro, Zihui Zhao","submitted_at":"2019-08-08T16:40:29Z","abstract_excerpt":"The present paper, along with its companion [Hofmann, Martell, Mayboroda, Toro, Zhao, arXiv:1710.06157], establishes the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. We settle the question of whether (quantitative) absolute continuity of the elliptic measure with respect to the surface measure and uniform rectifiability of the boundary are equivalent, in an optimal class of divergence form elliptic operators satisfying a suitable Carleson measure condition. The result can be viewed as a quantitative analogue of the Wiene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03161","kind":"arxiv","version":2},"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/1908.03161/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:30:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Xp250JO29GxYNVovH79nrkaReXwhFQgjLFUb334xyYMMc+Cf56BtblZCBMiEzDx+zBhBrOivp9egeBYBz1tCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:48:10.301787Z"},"content_sha256":"79f67ba3a40ab428081e0e99d521c1939127f7282e176248da3ea83f551afb2c","schema_version":"1.0","event_id":"sha256:79f67ba3a40ab428081e0e99d521c1939127f7282e176248da3ea83f551afb2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ODIHZA2XDOU4GIYS6RUD32PDN/bundle.json","state_url":"https://pith.science/pith/2ODIHZA2XDOU4GIYS6RUD32PDN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ODIHZA2XDOU4GIYS6RUD32PDN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T15:48:10Z","links":{"resolver":"https://pith.science/pith/2ODIHZA2XDOU4GIYS6RUD32PDN","bundle":"https://pith.science/pith/2ODIHZA2XDOU4GIYS6RUD32PDN/bundle.json","state":"https://pith.science/pith/2ODIHZA2XDOU4GIYS6RUD32PDN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ODIHZA2XDOU4GIYS6RUD32PDN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:2ODIHZA2XDOU4GIYS6RUD32PDN","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":"488dd3b98d378e6466be5c3f72555537c094ff9978dff905aaf9da3c8279ccbd","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-08T16:40:29Z","title_canon_sha256":"3ae45dfcc0f4ac4d97e26645ea9da07403977c18e205c3d8b2c1547022f37e0f"},"schema_version":"1.0","source":{"id":"1908.03161","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03161","created_at":"2026-07-05T00:30:20Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03161v2","created_at":"2026-07-05T00:30:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03161","created_at":"2026-07-05T00:30:20Z"},{"alias_kind":"pith_short_12","alias_value":"2ODIHZA2XDOU","created_at":"2026-07-05T00:30:20Z"},{"alias_kind":"pith_short_16","alias_value":"2ODIHZA2XDOU4GIY","created_at":"2026-07-05T00:30:20Z"},{"alias_kind":"pith_short_8","alias_value":"2ODIHZA2","created_at":"2026-07-05T00:30:20Z"}],"graph_snapshots":[{"event_id":"sha256:79f67ba3a40ab428081e0e99d521c1939127f7282e176248da3ea83f551afb2c","target":"graph","created_at":"2026-07-05T00:30:20Z","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/1908.03161/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The present paper, along with its companion [Hofmann, Martell, Mayboroda, Toro, Zhao, arXiv:1710.06157], establishes the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. We settle the question of whether (quantitative) absolute continuity of the elliptic measure with respect to the surface measure and uniform rectifiability of the boundary are equivalent, in an optimal class of divergence form elliptic operators satisfying a suitable Carleson measure condition. The result can be viewed as a quantitative analogue of the Wiene","authors_text":"Jos\\'e Mar\\'ia Martell, Steve Hofmann, Svitlana Mayboroda, Tatiana Toro, Zihui Zhao","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-08T16:40:29Z","title":"Uniform rectifiability and elliptic operators satisfying a Carleson measure condition. Part II: The large constant case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03161","kind":"arxiv","version":2},"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":"sha256:169d7e1e97d0136fb6af1a6818f3bf7320184eb7967bb1a35431f416ad8eb506","target":"record","created_at":"2026-07-05T00:30:20Z","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":"488dd3b98d378e6466be5c3f72555537c094ff9978dff905aaf9da3c8279ccbd","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-08T16:40:29Z","title_canon_sha256":"3ae45dfcc0f4ac4d97e26645ea9da07403977c18e205c3d8b2c1547022f37e0f"},"schema_version":"1.0","source":{"id":"1908.03161","kind":"arxiv","version":2}},"canonical_sha256":"d38683e41ab8dd4e191897a341ef4f1b7794e1ece01a60af4652d36eb93ccb76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d38683e41ab8dd4e191897a341ef4f1b7794e1ece01a60af4652d36eb93ccb76","first_computed_at":"2026-07-05T00:30:20.401830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:30:20.401830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bUoPA4X3UdL2LQ3Yg+OKWwf08XzhDsPkJBLRq1BRaTJOICBs1JVNU4yTDak6xDjGlujX/2PKsFpGaLRAVed1DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:30:20.402235Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03161","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:169d7e1e97d0136fb6af1a6818f3bf7320184eb7967bb1a35431f416ad8eb506","sha256:79f67ba3a40ab428081e0e99d521c1939127f7282e176248da3ea83f551afb2c"],"state_sha256":"437c406ad834f6c9afe5077d3304d356b3b01afb6d81a5f655d28fe2b6ffe359"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lgFELP6RveUOC5J2hq7u1QRSNBuFFcTl6fo7QdWMIYnfzz7CVCmvazbc2ZydRMCLvT2c3WNgugPUwJTyqVANBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T15:48:10.330764Z","bundle_sha256":"6a1a3634e8cdaac9bdbc3fab7eea61b1c8de38584b92d0d1c5c5c62718ce66ce"}}