{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:PWS7KKAEAX62Q2DNYQ2IAOXIUE","short_pith_number":"pith:PWS7KKAE","canonical_record":{"source":{"id":"1908.04050","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-12T08:27:40Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"a09b1e3075a18579f016c78f0e4600b9163793cb99137d0c2abe700d6ad47199","abstract_canon_sha256":"ef0e1961be012c76faf7e7bffe91b10f188392374b802754f20f73b6ed095748"},"schema_version":"1.0"},"canonical_sha256":"7da5f5280405fda8686dc434803ae8a1012be0123cfee048a0c17f45da95baa0","source":{"kind":"arxiv","id":"1908.04050","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04050","created_at":"2026-07-05T03:15:26Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04050v1","created_at":"2026-07-05T03:15:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04050","created_at":"2026-07-05T03:15:26Z"},{"alias_kind":"pith_short_12","alias_value":"PWS7KKAEAX62","created_at":"2026-07-05T03:15:26Z"},{"alias_kind":"pith_short_16","alias_value":"PWS7KKAEAX62Q2DN","created_at":"2026-07-05T03:15:26Z"},{"alias_kind":"pith_short_8","alias_value":"PWS7KKAE","created_at":"2026-07-05T03:15:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:PWS7KKAEAX62Q2DNYQ2IAOXIUE","target":"record","payload":{"canonical_record":{"source":{"id":"1908.04050","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-12T08:27:40Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"a09b1e3075a18579f016c78f0e4600b9163793cb99137d0c2abe700d6ad47199","abstract_canon_sha256":"ef0e1961be012c76faf7e7bffe91b10f188392374b802754f20f73b6ed095748"},"schema_version":"1.0"},"canonical_sha256":"7da5f5280405fda8686dc434803ae8a1012be0123cfee048a0c17f45da95baa0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:15:26.421027Z","signature_b64":"bDg44jaCCICawqqk9RzFQ1RDMfQQplOJXdEUCz26WFbUtYHGXj8apEvKPo5WIVzequFNtpYhtEoiddcs2YcdCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7da5f5280405fda8686dc434803ae8a1012be0123cfee048a0c17f45da95baa0","last_reissued_at":"2026-07-05T03:15:26.420670Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:15:26.420670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.04050","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:15:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gLvISoRNtYsKIj4VP5K24z898Equhi6M6ZwAPGX42juWfn2ZPhWroPM1ZHqgSwvOyWSI3MyxMYU2Jh/HuYrVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:29:05.538939Z"},"content_sha256":"88f80707483de480cfe11878225de6861c8c2b2d9233025b11cdb8eed7b2bb76","schema_version":"1.0","event_id":"sha256:88f80707483de480cfe11878225de6861c8c2b2d9233025b11cdb8eed7b2bb76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:PWS7KKAEAX62Q2DNYQ2IAOXIUE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Bilinear Strategy for Calder\\'on's Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Felipe Ponce-Vanegas (Basque Center for Applied Mathematics)","submitted_at":"2019-08-12T08:27:40Z","abstract_excerpt":"Electrical Impedance Imaging would suffer a serious obstruction if for two different conductivities the potential and current measured at the boundary were the same. The Calder\\'on's problem is to decide whether the conductivity is indeed uniquely determined by the data at the boundary. In $\\mathbb{R}^d$, for $d=5,6$, we show that uniqueness holds when the conductivity is in $W^{1+\\frac{d-5}{2p}+, p}(\\Omega)$, for $d\\le p <\\infty$. This improves on recent results of Haberman, and of Ham, Kwon and Lee. The main novelty of the proof is an extension of Tao's bilinear Theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04050","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.04050/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":"2026-07-05T03:15:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7QI9soweL4us3yEuM1OFsT7KqFnFCavC7o/wWLGCgd8GAXVxeyfa3UM/o1gpiTce54QiyFrqLE7vk06Tz3QZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:29:05.539845Z"},"content_sha256":"9710d8dab2a0cd35b4ce396df2684a4c6a638158d358811375e6bb5a3c7c7362","schema_version":"1.0","event_id":"sha256:9710d8dab2a0cd35b4ce396df2684a4c6a638158d358811375e6bb5a3c7c7362"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PWS7KKAEAX62Q2DNYQ2IAOXIUE/bundle.json","state_url":"https://pith.science/pith/PWS7KKAEAX62Q2DNYQ2IAOXIUE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PWS7KKAEAX62Q2DNYQ2IAOXIUE/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":"2026-08-16T10:29:05Z","links":{"resolver":"https://pith.science/pith/PWS7KKAEAX62Q2DNYQ2IAOXIUE","bundle":"https://pith.science/pith/PWS7KKAEAX62Q2DNYQ2IAOXIUE/bundle.json","state":"https://pith.science/pith/PWS7KKAEAX62Q2DNYQ2IAOXIUE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PWS7KKAEAX62Q2DNYQ2IAOXIUE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PWS7KKAEAX62Q2DNYQ2IAOXIUE","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":"ef0e1961be012c76faf7e7bffe91b10f188392374b802754f20f73b6ed095748","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-12T08:27:40Z","title_canon_sha256":"a09b1e3075a18579f016c78f0e4600b9163793cb99137d0c2abe700d6ad47199"},"schema_version":"1.0","source":{"id":"1908.04050","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04050","created_at":"2026-07-05T03:15:26Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04050v1","created_at":"2026-07-05T03:15:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04050","created_at":"2026-07-05T03:15:26Z"},{"alias_kind":"pith_short_12","alias_value":"PWS7KKAEAX62","created_at":"2026-07-05T03:15:26Z"},{"alias_kind":"pith_short_16","alias_value":"PWS7KKAEAX62Q2DN","created_at":"2026-07-05T03:15:26Z"},{"alias_kind":"pith_short_8","alias_value":"PWS7KKAE","created_at":"2026-07-05T03:15:26Z"}],"graph_snapshots":[{"event_id":"sha256:9710d8dab2a0cd35b4ce396df2684a4c6a638158d358811375e6bb5a3c7c7362","target":"graph","created_at":"2026-07-05T03:15:26Z","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/1908.04050/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Electrical Impedance Imaging would suffer a serious obstruction if for two different conductivities the potential and current measured at the boundary were the same. The Calder\\'on's problem is to decide whether the conductivity is indeed uniquely determined by the data at the boundary. In $\\mathbb{R}^d$, for $d=5,6$, we show that uniqueness holds when the conductivity is in $W^{1+\\frac{d-5}{2p}+, p}(\\Omega)$, for $d\\le p <\\infty$. This improves on recent results of Haberman, and of Ham, Kwon and Lee. The main novelty of the proof is an extension of Tao's bilinear Theorem.","authors_text":"Felipe Ponce-Vanegas (Basque Center for Applied Mathematics)","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-12T08:27:40Z","title":"The Bilinear Strategy for Calder\\'on's Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04050","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":"sha256:88f80707483de480cfe11878225de6861c8c2b2d9233025b11cdb8eed7b2bb76","target":"record","created_at":"2026-07-05T03:15:26Z","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":"ef0e1961be012c76faf7e7bffe91b10f188392374b802754f20f73b6ed095748","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-12T08:27:40Z","title_canon_sha256":"a09b1e3075a18579f016c78f0e4600b9163793cb99137d0c2abe700d6ad47199"},"schema_version":"1.0","source":{"id":"1908.04050","kind":"arxiv","version":1}},"canonical_sha256":"7da5f5280405fda8686dc434803ae8a1012be0123cfee048a0c17f45da95baa0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7da5f5280405fda8686dc434803ae8a1012be0123cfee048a0c17f45da95baa0","first_computed_at":"2026-07-05T03:15:26.420670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:15:26.420670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bDg44jaCCICawqqk9RzFQ1RDMfQQplOJXdEUCz26WFbUtYHGXj8apEvKPo5WIVzequFNtpYhtEoiddcs2YcdCw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:15:26.421027Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.04050","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88f80707483de480cfe11878225de6861c8c2b2d9233025b11cdb8eed7b2bb76","sha256:9710d8dab2a0cd35b4ce396df2684a4c6a638158d358811375e6bb5a3c7c7362"],"state_sha256":"72f7a2c6ec612c9718bf13f6696b396cd51c3b8c72778a538591d697f10d0f59"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z1YSbLPt2yzrHCuebjpyM6kDtN6VDQQHC6PqvvryQKN/4Sb3joipIOCbOmdSoKMqskyW7Uq3q13FPFtUF8yFBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T10:29:05.546691Z","bundle_sha256":"a8617f3b75fa8aa53aec3edabfa099f479ae2c04e8fd51865169a1aa302cf927"}}