{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GEXSR776JWQOHPLQ4PY5YNHBYU","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":"6fa1bdf017260d3b76b389025e0155dc2b843f799ffbd8f950b59c88343b0091","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-24T20:33:35Z","title_canon_sha256":"9ae693b6897059525e74019fcd0d55270b8953fcf2462fbb65aaf1f4e3723c4b"},"schema_version":"1.0","source":{"id":"1503.07190","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07190","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07190v2","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07190","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"GEXSR776JWQO","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GEXSR776JWQOHPLQ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GEXSR776","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:58766238c33ac6e6952b1a3cc3fa2db3f810941c34e65ec459ec6f5b0348588c","target":"graph","created_at":"2026-05-18T01:23:33Z","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 derive explicit reconstruction formulas for the attenuated geodesic X-ray transform over functions and, in the case of non-vanishing attenuation, vector fields, on a class of simple Riemannian surfaces with boundary. These formulas partly rely on new explicit approaches to construct continuous right-inverses for backprojection operators (and, in turn, holomorphic integrating factors), which were previously unavailable in a systematic form. The reconstruction of functions is presented in two ways, the latter one being motivated by numerical considerations and successfully implemented at the ","authors_text":"Fran\\c{c}ois Monard","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-24T20:33:35Z","title":"Inversion of the attenuated geodesic X-ray transform over functions and vector fields on simple surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07190","kind":"arxiv","version":2},"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":"sha256:56b3a635e9ece72dff0965307a128a1d7840249da80f9e606d76a08d54fc3f74","target":"record","created_at":"2026-05-18T01:23:33Z","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":"6fa1bdf017260d3b76b389025e0155dc2b843f799ffbd8f950b59c88343b0091","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-24T20:33:35Z","title_canon_sha256":"9ae693b6897059525e74019fcd0d55270b8953fcf2462fbb65aaf1f4e3723c4b"},"schema_version":"1.0","source":{"id":"1503.07190","kind":"arxiv","version":2}},"canonical_sha256":"312f28fffe4da0e3bd70e3f1dc34e1c51386e141078d058ae7ae5ab57c445c13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"312f28fffe4da0e3bd70e3f1dc34e1c51386e141078d058ae7ae5ab57c445c13","first_computed_at":"2026-05-18T01:23:33.579707Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:33.579707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xDWOIjob+m40hRn+uBTDvziFk4zq0acLmOTo5iL9TrgtfgOiBlD0Mzmrgom16fWbASBSX79qfZAiuTNXVaCqAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:33.580718Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.07190","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56b3a635e9ece72dff0965307a128a1d7840249da80f9e606d76a08d54fc3f74","sha256:58766238c33ac6e6952b1a3cc3fa2db3f810941c34e65ec459ec6f5b0348588c"],"state_sha256":"1231213f0496dc84eda1f669e406f1c970d3ca910e88891666fe543737a0ae7d"}