{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:O4MNC35QAFKNFWIU73WHLI4GTM","short_pith_number":"pith:O4MNC35Q","canonical_record":{"source":{"id":"1612.02650","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-08T14:11:43Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"9fd27faada2db8c3c93a4b490eed570031bc009eb4c6ec950dbc063a98a0f5ac","abstract_canon_sha256":"6c58dd8ce57d9476085011d9c211f3c5c363bcf2b7b0a5e84a627c68d7a1f7c0"},"schema_version":"1.0"},"canonical_sha256":"7718d16fb00154d2d914feec75a3869b3579461c9aca218619bff642339a6167","source":{"kind":"arxiv","id":"1612.02650","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02650","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02650v3","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02650","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"O4MNC35QAFKN","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"O4MNC35QAFKNFWIU","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"O4MNC35Q","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:O4MNC35QAFKNFWIU73WHLI4GTM","target":"record","payload":{"canonical_record":{"source":{"id":"1612.02650","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-08T14:11:43Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"9fd27faada2db8c3c93a4b490eed570031bc009eb4c6ec950dbc063a98a0f5ac","abstract_canon_sha256":"6c58dd8ce57d9476085011d9c211f3c5c363bcf2b7b0a5e84a627c68d7a1f7c0"},"schema_version":"1.0"},"canonical_sha256":"7718d16fb00154d2d914feec75a3869b3579461c9aca218619bff642339a6167","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:18.054468Z","signature_b64":"M2+BoRwgg8lGieg6u7jyX6w5HpAeBfH0kq9/6cbMwMtE3j6aTwgO1ZFK01G4XnkXL4lB/MGMjPIdBnwpBgA7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7718d16fb00154d2d914feec75a3869b3579461c9aca218619bff642339a6167","last_reissued_at":"2026-05-18T00:41:18.053768Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:18.053768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.02650","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qUWnqPq923eaCAWZSqDbrlqUwfQLo7LlrzP4rl3bAco8/QlFrPBWO254EB9ncKhdd1idhcO7SgmVrmBo6qSjAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:12:57.478778Z"},"content_sha256":"713d2d790f5bf4fc3f64ae4e14e2552e8eb988b1b7b36f403e665f5d1b23e4f5","schema_version":"1.0","event_id":"sha256:713d2d790f5bf4fc3f64ae4e14e2552e8eb988b1b7b36f403e665f5d1b23e4f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:O4MNC35QAFKNFWIU73WHLI4GTM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform rectifiability, elliptic measure, square functions, and $\\varepsilon$-approximability via an ACF monotonicity formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"John Garnett, Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa","submitted_at":"2016-12-08T14:11:43Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{R}^{n+1}$, $n\\geq2$, be an open set with Ahlfors-David regular boundary that satisfies the corkscrew condition. We consider a uniformly elliptic operator $L$ in divergence form associated with a matrix $A$ with real, merely bounded and possibly non-symmetric coefficients, which are also locally Lipschitz and satisfy suitable Carleson type estimates. In this paper we show that if $L^*$ is the operator in divergence form associated with the transpose matrix of $A$, then $\\partial\\Omega$ is uniformly $n$-rectifiable if and only if every bounded solution of $Lu=0$ and eve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02650","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MoBSyBdc9dBMnxgWmbEYW7nvn8hrVxCkZcF6vNPd22aOg7dRGo+7hKYViAJ3e6z/TedDZOdPinqiBZ6+ze0jAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:12:57.479511Z"},"content_sha256":"dc9154a152ace2ac4ab3804daff6c8eff238eb57529ea00520d772c99f99a237","schema_version":"1.0","event_id":"sha256:dc9154a152ace2ac4ab3804daff6c8eff238eb57529ea00520d772c99f99a237"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O4MNC35QAFKNFWIU73WHLI4GTM/bundle.json","state_url":"https://pith.science/pith/O4MNC35QAFKNFWIU73WHLI4GTM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O4MNC35QAFKNFWIU73WHLI4GTM/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":"2026-05-26T11:12:57Z","links":{"resolver":"https://pith.science/pith/O4MNC35QAFKNFWIU73WHLI4GTM","bundle":"https://pith.science/pith/O4MNC35QAFKNFWIU73WHLI4GTM/bundle.json","state":"https://pith.science/pith/O4MNC35QAFKNFWIU73WHLI4GTM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O4MNC35QAFKNFWIU73WHLI4GTM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:O4MNC35QAFKNFWIU73WHLI4GTM","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":"6c58dd8ce57d9476085011d9c211f3c5c363bcf2b7b0a5e84a627c68d7a1f7c0","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-08T14:11:43Z","title_canon_sha256":"9fd27faada2db8c3c93a4b490eed570031bc009eb4c6ec950dbc063a98a0f5ac"},"schema_version":"1.0","source":{"id":"1612.02650","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02650","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02650v3","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02650","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"O4MNC35QAFKN","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"O4MNC35QAFKNFWIU","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"O4MNC35Q","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:dc9154a152ace2ac4ab3804daff6c8eff238eb57529ea00520d772c99f99a237","target":"graph","created_at":"2026-05-18T00:41:18Z","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":"Let $\\Omega\\subset\\mathbb{R}^{n+1}$, $n\\geq2$, be an open set with Ahlfors-David regular boundary that satisfies the corkscrew condition. We consider a uniformly elliptic operator $L$ in divergence form associated with a matrix $A$ with real, merely bounded and possibly non-symmetric coefficients, which are also locally Lipschitz and satisfy suitable Carleson type estimates. In this paper we show that if $L^*$ is the operator in divergence form associated with the transpose matrix of $A$, then $\\partial\\Omega$ is uniformly $n$-rectifiable if and only if every bounded solution of $Lu=0$ and eve","authors_text":"John Garnett, Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-08T14:11:43Z","title":"Uniform rectifiability, elliptic measure, square functions, and $\\varepsilon$-approximability via an ACF monotonicity formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02650","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":"sha256:713d2d790f5bf4fc3f64ae4e14e2552e8eb988b1b7b36f403e665f5d1b23e4f5","target":"record","created_at":"2026-05-18T00:41:18Z","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":"6c58dd8ce57d9476085011d9c211f3c5c363bcf2b7b0a5e84a627c68d7a1f7c0","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-08T14:11:43Z","title_canon_sha256":"9fd27faada2db8c3c93a4b490eed570031bc009eb4c6ec950dbc063a98a0f5ac"},"schema_version":"1.0","source":{"id":"1612.02650","kind":"arxiv","version":3}},"canonical_sha256":"7718d16fb00154d2d914feec75a3869b3579461c9aca218619bff642339a6167","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7718d16fb00154d2d914feec75a3869b3579461c9aca218619bff642339a6167","first_computed_at":"2026-05-18T00:41:18.053768Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:18.053768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M2+BoRwgg8lGieg6u7jyX6w5HpAeBfH0kq9/6cbMwMtE3j6aTwgO1ZFK01G4XnkXL4lB/MGMjPIdBnwpBgA7Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:18.054468Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02650","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:713d2d790f5bf4fc3f64ae4e14e2552e8eb988b1b7b36f403e665f5d1b23e4f5","sha256:dc9154a152ace2ac4ab3804daff6c8eff238eb57529ea00520d772c99f99a237"],"state_sha256":"7db8f4ae2f71b2bd1b05d9fe6ec208786659b4e85e8b9df3aa11d49701658d3c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S9J8wgii2QvKrYVEY0q+6JgvR/R3Kohw76dDOV1Ee098XMhNTgue1O6wI94eNu4MkJDLAAe8npMkNLfLe+rABQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:12:57.483160Z","bundle_sha256":"a3b31d1197d3f4596389385ce85ce5ab77d334bdafda9ac4695addff6ba123f2"}}