{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KQ76TPBMT24WRZMFHLA5X4AXLS","short_pith_number":"pith:KQ76TPBM","canonical_record":{"source":{"id":"1612.01568","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-05T21:45:25Z","cross_cats_sorted":[],"title_canon_sha256":"92deea92deef7bac977137587fb365e6538c1256fde9278f2e5e409848c66aeb","abstract_canon_sha256":"9bc92bfafb87ceda0c03e71a042f763620c645a718e7d4dcde279ca610b53a98"},"schema_version":"1.0"},"canonical_sha256":"543fe9bc2c9eb968e5853ac1dbf0175cb24acf4202ebc0febcc6b5eb85596917","source":{"kind":"arxiv","id":"1612.01568","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01568","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01568v4","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01568","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"KQ76TPBMT24W","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KQ76TPBMT24WRZMF","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KQ76TPBM","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KQ76TPBMT24WRZMFHLA5X4AXLS","target":"record","payload":{"canonical_record":{"source":{"id":"1612.01568","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-05T21:45:25Z","cross_cats_sorted":[],"title_canon_sha256":"92deea92deef7bac977137587fb365e6538c1256fde9278f2e5e409848c66aeb","abstract_canon_sha256":"9bc92bfafb87ceda0c03e71a042f763620c645a718e7d4dcde279ca610b53a98"},"schema_version":"1.0"},"canonical_sha256":"543fe9bc2c9eb968e5853ac1dbf0175cb24acf4202ebc0febcc6b5eb85596917","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:42.526187Z","signature_b64":"DPgSslMWCXvgmmiDNiCLN/QCnTl6pxiRyTk1lKX34G4i4H8UXdlZh6A+I0ZuGPdjzUmje0PvQuJmqwlLV73rBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"543fe9bc2c9eb968e5853ac1dbf0175cb24acf4202ebc0febcc6b5eb85596917","last_reissued_at":"2026-05-18T00:19:42.525515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:42.525515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.01568","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:19:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t42h6AjE+CBqtXgWzG6ysplB0R+6g1ZGfd4rB6u+e32R96pcxmjYxA/0eP5Ajz1pTCvq238jxaTUWmtTgYchCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T03:25:30.239155Z"},"content_sha256":"19bdbc7111d133c25eb4eb9553de167b707d3979c7e3731423e3c08afd823540","schema_version":"1.0","event_id":"sha256:19bdbc7111d133c25eb4eb9553de167b707d3979c7e3731423e3c08afd823540"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KQ76TPBMT24WRZMFHLA5X4AXLS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity theory for solutions to second order elliptic operators with complex coefficients and the $L^p$ Dirichlet problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jill Pipher, Martin Dindo\\v{s}","submitted_at":"2016-12-05T21:45:25Z","abstract_excerpt":"We establish a new theory of regularity for elliptic complex valued second order equations of the form $\\mathcal L=$div$A(\\nabla\\cdot)$, when the coefficients of the matrix $A$ satisfy a natural algebraic condition, a strengthened version of a condition known in the literature as $L^p$-dissipativity. Precisely, the regularity result is a reverse H\\\"older condition for $L^p$ averages of solutions on interior balls, and serves as a replacement for the De Giorgi - Nash - Moser regularity of solutions to real-valued divergence form elliptic operators. In a series of papers, Cialdea and Maz'ya stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01568","kind":"arxiv","version":4},"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":"2026-05-18T00:19:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dawdh5fwbO1vUgTApg/8dwR9YFNIij4l/79kjlaD9U8W05hW9nHzQYSBvP5Cff3n5T6j+jhSzJGIMW90W8EnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T03:25:30.239872Z"},"content_sha256":"79ab621f0ee59f129258966c61c6844c634de061577cb21befaf5a69d4a10bb2","schema_version":"1.0","event_id":"sha256:79ab621f0ee59f129258966c61c6844c634de061577cb21befaf5a69d4a10bb2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KQ76TPBMT24WRZMFHLA5X4AXLS/bundle.json","state_url":"https://pith.science/pith/KQ76TPBMT24WRZMFHLA5X4AXLS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KQ76TPBMT24WRZMFHLA5X4AXLS/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":"2026-06-10T03:25:30Z","links":{"resolver":"https://pith.science/pith/KQ76TPBMT24WRZMFHLA5X4AXLS","bundle":"https://pith.science/pith/KQ76TPBMT24WRZMFHLA5X4AXLS/bundle.json","state":"https://pith.science/pith/KQ76TPBMT24WRZMFHLA5X4AXLS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KQ76TPBMT24WRZMFHLA5X4AXLS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KQ76TPBMT24WRZMFHLA5X4AXLS","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":"9bc92bfafb87ceda0c03e71a042f763620c645a718e7d4dcde279ca610b53a98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-05T21:45:25Z","title_canon_sha256":"92deea92deef7bac977137587fb365e6538c1256fde9278f2e5e409848c66aeb"},"schema_version":"1.0","source":{"id":"1612.01568","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01568","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01568v4","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01568","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"KQ76TPBMT24W","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KQ76TPBMT24WRZMF","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KQ76TPBM","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:79ab621f0ee59f129258966c61c6844c634de061577cb21befaf5a69d4a10bb2","target":"graph","created_at":"2026-05-18T00:19:42Z","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":"We establish a new theory of regularity for elliptic complex valued second order equations of the form $\\mathcal L=$div$A(\\nabla\\cdot)$, when the coefficients of the matrix $A$ satisfy a natural algebraic condition, a strengthened version of a condition known in the literature as $L^p$-dissipativity. Precisely, the regularity result is a reverse H\\\"older condition for $L^p$ averages of solutions on interior balls, and serves as a replacement for the De Giorgi - Nash - Moser regularity of solutions to real-valued divergence form elliptic operators. In a series of papers, Cialdea and Maz'ya stud","authors_text":"Jill Pipher, Martin Dindo\\v{s}","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-05T21:45:25Z","title":"Regularity theory for solutions to second order elliptic operators with complex coefficients and the $L^p$ Dirichlet problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01568","kind":"arxiv","version":4},"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":"sha256:19bdbc7111d133c25eb4eb9553de167b707d3979c7e3731423e3c08afd823540","target":"record","created_at":"2026-05-18T00:19:42Z","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":"9bc92bfafb87ceda0c03e71a042f763620c645a718e7d4dcde279ca610b53a98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-05T21:45:25Z","title_canon_sha256":"92deea92deef7bac977137587fb365e6538c1256fde9278f2e5e409848c66aeb"},"schema_version":"1.0","source":{"id":"1612.01568","kind":"arxiv","version":4}},"canonical_sha256":"543fe9bc2c9eb968e5853ac1dbf0175cb24acf4202ebc0febcc6b5eb85596917","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"543fe9bc2c9eb968e5853ac1dbf0175cb24acf4202ebc0febcc6b5eb85596917","first_computed_at":"2026-05-18T00:19:42.525515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:42.525515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DPgSslMWCXvgmmiDNiCLN/QCnTl6pxiRyTk1lKX34G4i4H8UXdlZh6A+I0ZuGPdjzUmje0PvQuJmqwlLV73rBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:42.526187Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.01568","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19bdbc7111d133c25eb4eb9553de167b707d3979c7e3731423e3c08afd823540","sha256:79ab621f0ee59f129258966c61c6844c634de061577cb21befaf5a69d4a10bb2"],"state_sha256":"dd63c9a055afc2d08ecbf497ff74828892874bb415c3b84bf4aa08a94fbe9404"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DqZS2uYFzvh/dRX9qoA9zHzVHOnXHTwVOkNE9t7Hx0zsZt8A69dCPPIw5U3eNc8dNqf0iNdzKixMXaP2FFaTAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T03:25:30.244002Z","bundle_sha256":"70c151cc1acf0200e03a7d8955620a890b342d8bb1551e63b368198a5d03cc83"}}