{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:J5AFPYWJH27CTTYNWENAUB6KCG","short_pith_number":"pith:J5AFPYWJ","canonical_record":{"source":{"id":"2112.03480","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-12-07T03:57:21Z","cross_cats_sorted":[],"title_canon_sha256":"f50bf06b1255b883d6d4de299aaa440cb64db0f5b0fc42865038ca0689a02253","abstract_canon_sha256":"ec18c67e066b15c0ae1cca23680e672513cea5585276da0e3690dc3d4af178a8"},"schema_version":"1.0"},"canonical_sha256":"4f4057e2c93ebe29cf0db11a0a07ca11a0f4302a500dc06218b1079f64ef36d2","source":{"kind":"arxiv","id":"2112.03480","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.03480","created_at":"2026-07-05T12:06:56Z"},{"alias_kind":"arxiv_version","alias_value":"2112.03480v1","created_at":"2026-07-05T12:06:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.03480","created_at":"2026-07-05T12:06:56Z"},{"alias_kind":"pith_short_12","alias_value":"J5AFPYWJH27C","created_at":"2026-07-05T12:06:56Z"},{"alias_kind":"pith_short_16","alias_value":"J5AFPYWJH27CTTYN","created_at":"2026-07-05T12:06:56Z"},{"alias_kind":"pith_short_8","alias_value":"J5AFPYWJ","created_at":"2026-07-05T12:06:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:J5AFPYWJH27CTTYNWENAUB6KCG","target":"record","payload":{"canonical_record":{"source":{"id":"2112.03480","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-12-07T03:57:21Z","cross_cats_sorted":[],"title_canon_sha256":"f50bf06b1255b883d6d4de299aaa440cb64db0f5b0fc42865038ca0689a02253","abstract_canon_sha256":"ec18c67e066b15c0ae1cca23680e672513cea5585276da0e3690dc3d4af178a8"},"schema_version":"1.0"},"canonical_sha256":"4f4057e2c93ebe29cf0db11a0a07ca11a0f4302a500dc06218b1079f64ef36d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:06:56.485904Z","signature_b64":"1oNQOWAvNnELkQXuD66AvZuHvzDtp6oC3a26bbQGAdUUyZ/l88ZpEyat4thvTvEXYRn/212makbCOvAekPhmCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f4057e2c93ebe29cf0db11a0a07ca11a0f4302a500dc06218b1079f64ef36d2","last_reissued_at":"2026-07-05T12:06:56.485409Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:06:56.485409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.03480","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":"2026-07-05T12:06:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aNqU4iHvjZ7jJs3RNDbpzAQ4fIM2gk/vwgsufSRMVFgKn+vHccWobiHRqnuTawDpBTIJZ8M4A+jofqKKuw70DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T22:37:17.199101Z"},"content_sha256":"512ea12888eb8c9f160985210615c5a856bd7b2299994bf7a5f651bb54457db2","schema_version":"1.0","event_id":"sha256:512ea12888eb8c9f160985210615c5a856bd7b2299994bf7a5f651bb54457db2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:J5AFPYWJH27CTTYNWENAUB6KCG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional anisotropic Calder\\'on problem on closed Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ali Feizmohammadi, Gunther Uhlmann, Katya Krupchyk, Tuhin Ghosh","submitted_at":"2021-12-07T03:57:21Z","abstract_excerpt":"In this paper we solve the fractional anisotropic Calder\\'on problem on closed Riemannian manifolds of dimensions two and higher. Specifically, we prove that the knowledge of the local source-to-solution map for the fractional Laplacian, given on an arbitrary small open nonempty a priori known subset of a smooth closed connected Riemannian manifold, determines the Riemannian manifold up to an isometry. This can be viewed as a nonlocal analog of the anisotropic Calder\\'on problem in the setting of closed Riemannian manifolds, which is wide open in dimensions three and higher."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.03480","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/2112.03480/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":"2026-07-05T12:06:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Idxr4g17siEBIGUCebfDiCDTGVh14+AtIXoJPISRnp26Me19vuHRmcI0tmzdX9VfX1JifF6X+NAQpKZ0/w1ZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T22:37:17.199611Z"},"content_sha256":"c7e13a4a6d7af5f6cfd0aee4180a05c3c1b8123cd00294fa26dbabc5c3b9d7b6","schema_version":"1.0","event_id":"sha256:c7e13a4a6d7af5f6cfd0aee4180a05c3c1b8123cd00294fa26dbabc5c3b9d7b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J5AFPYWJH27CTTYNWENAUB6KCG/bundle.json","state_url":"https://pith.science/pith/J5AFPYWJH27CTTYNWENAUB6KCG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J5AFPYWJH27CTTYNWENAUB6KCG/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":"2026-08-08T22:37:17Z","links":{"resolver":"https://pith.science/pith/J5AFPYWJH27CTTYNWENAUB6KCG","bundle":"https://pith.science/pith/J5AFPYWJH27CTTYNWENAUB6KCG/bundle.json","state":"https://pith.science/pith/J5AFPYWJH27CTTYNWENAUB6KCG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J5AFPYWJH27CTTYNWENAUB6KCG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:J5AFPYWJH27CTTYNWENAUB6KCG","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":"ec18c67e066b15c0ae1cca23680e672513cea5585276da0e3690dc3d4af178a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-12-07T03:57:21Z","title_canon_sha256":"f50bf06b1255b883d6d4de299aaa440cb64db0f5b0fc42865038ca0689a02253"},"schema_version":"1.0","source":{"id":"2112.03480","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.03480","created_at":"2026-07-05T12:06:56Z"},{"alias_kind":"arxiv_version","alias_value":"2112.03480v1","created_at":"2026-07-05T12:06:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.03480","created_at":"2026-07-05T12:06:56Z"},{"alias_kind":"pith_short_12","alias_value":"J5AFPYWJH27C","created_at":"2026-07-05T12:06:56Z"},{"alias_kind":"pith_short_16","alias_value":"J5AFPYWJH27CTTYN","created_at":"2026-07-05T12:06:56Z"},{"alias_kind":"pith_short_8","alias_value":"J5AFPYWJ","created_at":"2026-07-05T12:06:56Z"}],"graph_snapshots":[{"event_id":"sha256:c7e13a4a6d7af5f6cfd0aee4180a05c3c1b8123cd00294fa26dbabc5c3b9d7b6","target":"graph","created_at":"2026-07-05T12:06:56Z","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/2112.03480/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we solve the fractional anisotropic Calder\\'on problem on closed Riemannian manifolds of dimensions two and higher. Specifically, we prove that the knowledge of the local source-to-solution map for the fractional Laplacian, given on an arbitrary small open nonempty a priori known subset of a smooth closed connected Riemannian manifold, determines the Riemannian manifold up to an isometry. This can be viewed as a nonlocal analog of the anisotropic Calder\\'on problem in the setting of closed Riemannian manifolds, which is wide open in dimensions three and higher.","authors_text":"Ali Feizmohammadi, Gunther Uhlmann, Katya Krupchyk, Tuhin Ghosh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-12-07T03:57:21Z","title":"Fractional anisotropic Calder\\'on problem on closed Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.03480","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":"sha256:512ea12888eb8c9f160985210615c5a856bd7b2299994bf7a5f651bb54457db2","target":"record","created_at":"2026-07-05T12:06:56Z","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":"ec18c67e066b15c0ae1cca23680e672513cea5585276da0e3690dc3d4af178a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-12-07T03:57:21Z","title_canon_sha256":"f50bf06b1255b883d6d4de299aaa440cb64db0f5b0fc42865038ca0689a02253"},"schema_version":"1.0","source":{"id":"2112.03480","kind":"arxiv","version":1}},"canonical_sha256":"4f4057e2c93ebe29cf0db11a0a07ca11a0f4302a500dc06218b1079f64ef36d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f4057e2c93ebe29cf0db11a0a07ca11a0f4302a500dc06218b1079f64ef36d2","first_computed_at":"2026-07-05T12:06:56.485409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:06:56.485409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1oNQOWAvNnELkQXuD66AvZuHvzDtp6oC3a26bbQGAdUUyZ/l88ZpEyat4thvTvEXYRn/212makbCOvAekPhmCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:06:56.485904Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.03480","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:512ea12888eb8c9f160985210615c5a856bd7b2299994bf7a5f651bb54457db2","sha256:c7e13a4a6d7af5f6cfd0aee4180a05c3c1b8123cd00294fa26dbabc5c3b9d7b6"],"state_sha256":"540c796b83f4e5488884407999436bf2fa36d4258ae33aa5165604ae4aced7b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yENMbpoIp8FVKaqyoPDVm+IH8tqB9h0+ZWX+KLBkK+o7HbMZmVw3k15psVVkW0Ymj9ncRCgiZ5AaMJAiMvSZCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T22:37:17.206497Z","bundle_sha256":"0225601ce3d4ca6b8bc827ff831e4cf9eb35a744f1ac430c8b19a8f657d8c781"}}