{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FGZQOYX7GHILRKQ4YQH5UGZEQK","short_pith_number":"pith:FGZQOYX7","canonical_record":{"source":{"id":"1604.00630","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-03T12:42:48Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"b622e1512373b207318f9fd7b3bb2c7ede8efc368ec79dac7ccc2c58b3f9101b","abstract_canon_sha256":"feb0bb70288474a4b4d87ed29f1c52db128e45272b2c53f81f787ac44544ef8a"},"schema_version":"1.0"},"canonical_sha256":"29b30762ff31d0b8aa1cc40fda1b248298055dec8e8ad4e18f3e4464a278f751","source":{"kind":"arxiv","id":"1604.00630","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00630","created_at":"2026-05-18T01:17:48Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00630v1","created_at":"2026-05-18T01:17:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00630","created_at":"2026-05-18T01:17:48Z"},{"alias_kind":"pith_short_12","alias_value":"FGZQOYX7GHIL","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FGZQOYX7GHILRKQ4","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FGZQOYX7","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FGZQOYX7GHILRKQ4YQH5UGZEQK","target":"record","payload":{"canonical_record":{"source":{"id":"1604.00630","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-03T12:42:48Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"b622e1512373b207318f9fd7b3bb2c7ede8efc368ec79dac7ccc2c58b3f9101b","abstract_canon_sha256":"feb0bb70288474a4b4d87ed29f1c52db128e45272b2c53f81f787ac44544ef8a"},"schema_version":"1.0"},"canonical_sha256":"29b30762ff31d0b8aa1cc40fda1b248298055dec8e8ad4e18f3e4464a278f751","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:48.866345Z","signature_b64":"L38NJCQniJL1cSF4y+0BVN+LTYJOiHP31XROXO6Q+56MxDlXnptFJ0tI3LbLK0zS9Up3XqbwXoWuuLuVCNzEBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29b30762ff31d0b8aa1cc40fda1b248298055dec8e8ad4e18f3e4464a278f751","last_reissued_at":"2026-05-18T01:17:48.865467Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:48.865467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.00630","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":"2026-05-18T01:17:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AkgTZBi3x5EZcs+YBIccvHFH0KT57csEWrMTYunnO7S9PxcoSlQrVq7LMmPQLhRBeJPbB2n570FGN6ebH/34BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:18:11.073568Z"},"content_sha256":"55056f89a806aa3a3a37d33e426ab7ac152104d22b5f6c282f430d942aac7385","schema_version":"1.0","event_id":"sha256:55056f89a806aa3a3a37d33e426ab7ac152104d22b5f6c282f430d942aac7385"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FGZQOYX7GHILRKQ4YQH5UGZEQK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Journey to the Center of the Earth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Gunther Uhlmann, Hanming Zhou","submitted_at":"2016-04-03T12:42:48Z","abstract_excerpt":"We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as geometry problems, the boundary rigidity problem and the lens rigidity problem. The boundary rigidity problem is whether we can determine a Riemannian metric of a compact Riemannian manifold with boundary by measuring the distance function between boundary points. The lens rigidity problem problem is to determine a Riemannian metric of a Riemannian manifold with boundary "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00630","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":"2026-05-18T01:17:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u3BnhEhed0+lp3+SisMC609BRp66WUOSIE53SAO21scPzYUb/6yEM2WDnJWDa4XS8umg4rBtLrvzoKSWcolaAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:18:11.073925Z"},"content_sha256":"d795975b52cb900b56f057d71b8007b0feae18fe767ab89f04ea484aa6bfe1aa","schema_version":"1.0","event_id":"sha256:d795975b52cb900b56f057d71b8007b0feae18fe767ab89f04ea484aa6bfe1aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FGZQOYX7GHILRKQ4YQH5UGZEQK/bundle.json","state_url":"https://pith.science/pith/FGZQOYX7GHILRKQ4YQH5UGZEQK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FGZQOYX7GHILRKQ4YQH5UGZEQK/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":"2026-05-28T08:18:11Z","links":{"resolver":"https://pith.science/pith/FGZQOYX7GHILRKQ4YQH5UGZEQK","bundle":"https://pith.science/pith/FGZQOYX7GHILRKQ4YQH5UGZEQK/bundle.json","state":"https://pith.science/pith/FGZQOYX7GHILRKQ4YQH5UGZEQK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FGZQOYX7GHILRKQ4YQH5UGZEQK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FGZQOYX7GHILRKQ4YQH5UGZEQK","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":"feb0bb70288474a4b4d87ed29f1c52db128e45272b2c53f81f787ac44544ef8a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-03T12:42:48Z","title_canon_sha256":"b622e1512373b207318f9fd7b3bb2c7ede8efc368ec79dac7ccc2c58b3f9101b"},"schema_version":"1.0","source":{"id":"1604.00630","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00630","created_at":"2026-05-18T01:17:48Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00630v1","created_at":"2026-05-18T01:17:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00630","created_at":"2026-05-18T01:17:48Z"},{"alias_kind":"pith_short_12","alias_value":"FGZQOYX7GHIL","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FGZQOYX7GHILRKQ4","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FGZQOYX7","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:d795975b52cb900b56f057d71b8007b0feae18fe767ab89f04ea484aa6bfe1aa","target":"graph","created_at":"2026-05-18T01:17:48Z","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 survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as geometry problems, the boundary rigidity problem and the lens rigidity problem. The boundary rigidity problem is whether we can determine a Riemannian metric of a compact Riemannian manifold with boundary by measuring the distance function between boundary points. The lens rigidity problem problem is to determine a Riemannian metric of a Riemannian manifold with boundary ","authors_text":"Gunther Uhlmann, Hanming Zhou","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-03T12:42:48Z","title":"Journey to the Center of the Earth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00630","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":"sha256:55056f89a806aa3a3a37d33e426ab7ac152104d22b5f6c282f430d942aac7385","target":"record","created_at":"2026-05-18T01:17:48Z","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":"feb0bb70288474a4b4d87ed29f1c52db128e45272b2c53f81f787ac44544ef8a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-03T12:42:48Z","title_canon_sha256":"b622e1512373b207318f9fd7b3bb2c7ede8efc368ec79dac7ccc2c58b3f9101b"},"schema_version":"1.0","source":{"id":"1604.00630","kind":"arxiv","version":1}},"canonical_sha256":"29b30762ff31d0b8aa1cc40fda1b248298055dec8e8ad4e18f3e4464a278f751","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29b30762ff31d0b8aa1cc40fda1b248298055dec8e8ad4e18f3e4464a278f751","first_computed_at":"2026-05-18T01:17:48.865467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:48.865467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L38NJCQniJL1cSF4y+0BVN+LTYJOiHP31XROXO6Q+56MxDlXnptFJ0tI3LbLK0zS9Up3XqbwXoWuuLuVCNzEBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:48.866345Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.00630","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55056f89a806aa3a3a37d33e426ab7ac152104d22b5f6c282f430d942aac7385","sha256:d795975b52cb900b56f057d71b8007b0feae18fe767ab89f04ea484aa6bfe1aa"],"state_sha256":"0c08b282d0b06f5613f4c660d9a77b9132abd60528710bc268a285c8663c67cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nKX+Z4ON4YW+AV7WzYB8KD+NeuxAdmdE2MtbnrrMdmnYJBvLGLQDJr1NF9k+8CNWnLRukkeiD0tRC7NoPGLiBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:18:11.075890Z","bundle_sha256":"163b5923186ed3eed482cd67ef9ee3963999f3bebfc81e21813adda58a1428ed"}}