{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5IL3ALH4SQJKBXEXCIIYXKACPM","short_pith_number":"pith:5IL3ALH4","canonical_record":{"source":{"id":"1712.04716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-13T11:36:27Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"4b306b63d79d925d82532287c9cf7beba379f5e8deb49831f23c76061d61a685","abstract_canon_sha256":"7b6b624d2247dff9cd2cd956601f647d3cd8c1871b9c7eb3cef9e597ff462d53"},"schema_version":"1.0"},"canonical_sha256":"ea17b02cfc9412a0dc9712118ba8027b054e85c176ac6fae95e01b07d28042ac","source":{"kind":"arxiv","id":"1712.04716","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04716","created_at":"2026-05-18T00:02:18Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04716v1","created_at":"2026-05-18T00:02:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04716","created_at":"2026-05-18T00:02:18Z"},{"alias_kind":"pith_short_12","alias_value":"5IL3ALH4SQJK","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5IL3ALH4SQJKBXEX","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5IL3ALH4","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5IL3ALH4SQJKBXEXCIIYXKACPM","target":"record","payload":{"canonical_record":{"source":{"id":"1712.04716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-13T11:36:27Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"4b306b63d79d925d82532287c9cf7beba379f5e8deb49831f23c76061d61a685","abstract_canon_sha256":"7b6b624d2247dff9cd2cd956601f647d3cd8c1871b9c7eb3cef9e597ff462d53"},"schema_version":"1.0"},"canonical_sha256":"ea17b02cfc9412a0dc9712118ba8027b054e85c176ac6fae95e01b07d28042ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:18.334038Z","signature_b64":"9mp0jSYfR0g4LAoDn0rUD2qHrwXwT2aTL/s60A+LenoxS75t0lQi1URurrk5DiwnEWhIUI5evdDu7aHV6pjmDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea17b02cfc9412a0dc9712118ba8027b054e85c176ac6fae95e01b07d28042ac","last_reissued_at":"2026-05-18T00:02:18.333470Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:18.333470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.04716","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":"2026-05-18T00:02:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wdJA966RN4qSV7Ty5uB3CM2t/H7IT7tivwD6KGSUuZq9wwUE54u4RanolFyYtf5ZLvuUD+qE0wNf823BFL4pBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T22:30:06.904115Z"},"content_sha256":"073aa4ff17a3a11f3f60cca075a7a6dd6c3951388da9c5e7393bb01f2b3caa3c","schema_version":"1.0","event_id":"sha256:073aa4ff17a3a11f3f60cca075a7a6dd6c3951388da9c5e7393bb01f2b3caa3c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5IL3ALH4SQJKBXEXCIIYXKACPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The linearized Calderon problem in transversally anisotropic geometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"David Dos Santos Ferreira, Matti Lassas, Mikko Salo, Tony Liimatainen, Yaroslav Kurylev","submitted_at":"2017-12-13T11:36:27Z","abstract_excerpt":"In this article we study the linearized anisotropic Calderon problem. In a compact manifold with boundary, this problem amounts to showing that products of harmonic functions form a complete set. Assuming that the manifold is transversally anisotropic, we show that the boundary measurements determine an FBI type transform at certain points in the transversal manifold. This leads to recovery of transversal singularities in the linearized problem. The method requires a geometric condition on the transversal manifold related to pairs of intersecting geodesics, but it does not involve the geodesic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04716","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":""},"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":"2026-05-18T00:02:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zQrRHN+MDN7zswRkQrkKBJBmY1YUJ4dmt00UUp5vy3a5570iS17yaGgFV/CXnIa2rBVdcHx9/V5/WOPpYbzEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T22:30:06.904478Z"},"content_sha256":"336ab68f7b2b6be199a1ebf71e3e5d365a40305ba610bce9fa7469e6775d3b99","schema_version":"1.0","event_id":"sha256:336ab68f7b2b6be199a1ebf71e3e5d365a40305ba610bce9fa7469e6775d3b99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5IL3ALH4SQJKBXEXCIIYXKACPM/bundle.json","state_url":"https://pith.science/pith/5IL3ALH4SQJKBXEXCIIYXKACPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5IL3ALH4SQJKBXEXCIIYXKACPM/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":"2026-06-03T22:30:06Z","links":{"resolver":"https://pith.science/pith/5IL3ALH4SQJKBXEXCIIYXKACPM","bundle":"https://pith.science/pith/5IL3ALH4SQJKBXEXCIIYXKACPM/bundle.json","state":"https://pith.science/pith/5IL3ALH4SQJKBXEXCIIYXKACPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5IL3ALH4SQJKBXEXCIIYXKACPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5IL3ALH4SQJKBXEXCIIYXKACPM","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":"7b6b624d2247dff9cd2cd956601f647d3cd8c1871b9c7eb3cef9e597ff462d53","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-13T11:36:27Z","title_canon_sha256":"4b306b63d79d925d82532287c9cf7beba379f5e8deb49831f23c76061d61a685"},"schema_version":"1.0","source":{"id":"1712.04716","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04716","created_at":"2026-05-18T00:02:18Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04716v1","created_at":"2026-05-18T00:02:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04716","created_at":"2026-05-18T00:02:18Z"},{"alias_kind":"pith_short_12","alias_value":"5IL3ALH4SQJK","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5IL3ALH4SQJKBXEX","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5IL3ALH4","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:336ab68f7b2b6be199a1ebf71e3e5d365a40305ba610bce9fa7469e6775d3b99","target":"graph","created_at":"2026-05-18T00:02:18Z","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":"In this article we study the linearized anisotropic Calderon problem. In a compact manifold with boundary, this problem amounts to showing that products of harmonic functions form a complete set. Assuming that the manifold is transversally anisotropic, we show that the boundary measurements determine an FBI type transform at certain points in the transversal manifold. This leads to recovery of transversal singularities in the linearized problem. The method requires a geometric condition on the transversal manifold related to pairs of intersecting geodesics, but it does not involve the geodesic","authors_text":"David Dos Santos Ferreira, Matti Lassas, Mikko Salo, Tony Liimatainen, Yaroslav Kurylev","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-13T11:36:27Z","title":"The linearized Calderon problem in transversally anisotropic geometries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04716","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":"sha256:073aa4ff17a3a11f3f60cca075a7a6dd6c3951388da9c5e7393bb01f2b3caa3c","target":"record","created_at":"2026-05-18T00:02:18Z","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":"7b6b624d2247dff9cd2cd956601f647d3cd8c1871b9c7eb3cef9e597ff462d53","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-13T11:36:27Z","title_canon_sha256":"4b306b63d79d925d82532287c9cf7beba379f5e8deb49831f23c76061d61a685"},"schema_version":"1.0","source":{"id":"1712.04716","kind":"arxiv","version":1}},"canonical_sha256":"ea17b02cfc9412a0dc9712118ba8027b054e85c176ac6fae95e01b07d28042ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea17b02cfc9412a0dc9712118ba8027b054e85c176ac6fae95e01b07d28042ac","first_computed_at":"2026-05-18T00:02:18.333470Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:18.333470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9mp0jSYfR0g4LAoDn0rUD2qHrwXwT2aTL/s60A+LenoxS75t0lQi1URurrk5DiwnEWhIUI5evdDu7aHV6pjmDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:18.334038Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.04716","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:073aa4ff17a3a11f3f60cca075a7a6dd6c3951388da9c5e7393bb01f2b3caa3c","sha256:336ab68f7b2b6be199a1ebf71e3e5d365a40305ba610bce9fa7469e6775d3b99"],"state_sha256":"4f709575ba6bfe73e7fb462072f7add97fdfe9b3f36cc6373f00563507a0ae0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Yl9D9/RYAm9+G+/qf9IxVGGt0v394FIqyOrd7pYTZXcE0xoborkJHs8UKLlPkW7RNPJ7bmrx0RWh6GbdyyeDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T22:30:06.906450Z","bundle_sha256":"206b31fba3e846ca07797569da4634800f5bed5ebb0c627c1c1d84a0587073e2"}}