{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6ARYZVYUKKUSGIT6YTE36YB5HE","short_pith_number":"pith:6ARYZVYU","canonical_record":{"source":{"id":"1610.09571","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-29T21:33:13Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"597f34128ff1cf6e70cd44df9e671c94ba522be9a14b33150849aa617face044","abstract_canon_sha256":"9789599292bde8ac0a5006d81ef2c50f7298eb506bd5ee086e10639b9214e600"},"schema_version":"1.0"},"canonical_sha256":"f0238cd71452a923227ec4c9bf603d391f3a4bc7c0283b76de54c90ce1c833a6","source":{"kind":"arxiv","id":"1610.09571","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09571","created_at":"2026-05-18T00:34:39Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09571v2","created_at":"2026-05-18T00:34:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09571","created_at":"2026-05-18T00:34:39Z"},{"alias_kind":"pith_short_12","alias_value":"6ARYZVYUKKUS","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6ARYZVYUKKUSGIT6","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6ARYZVYU","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6ARYZVYUKKUSGIT6YTE36YB5HE","target":"record","payload":{"canonical_record":{"source":{"id":"1610.09571","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-29T21:33:13Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"597f34128ff1cf6e70cd44df9e671c94ba522be9a14b33150849aa617face044","abstract_canon_sha256":"9789599292bde8ac0a5006d81ef2c50f7298eb506bd5ee086e10639b9214e600"},"schema_version":"1.0"},"canonical_sha256":"f0238cd71452a923227ec4c9bf603d391f3a4bc7c0283b76de54c90ce1c833a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:39.248070Z","signature_b64":"CGWliC6wSI8mWu3nczAQdQdl8AfE/oRMPEvcDtsr7uogUtR9xKn1mcby70m67e1Yo+F1s+2BuJQGPnik7Ge4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0238cd71452a923227ec4c9bf603d391f3a4bc7c0283b76de54c90ce1c833a6","last_reissued_at":"2026-05-18T00:34:39.247534Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:39.247534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.09571","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v9fXALnkiiIqu4dj6mmkZhIQYAK/reWNyYQRzFFYTbFf5zjqaejfVthk3fcxbDxSMZaiWG3UL2llkKiITsD0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T16:03:51.747197Z"},"content_sha256":"254bf93a3c054f1773a6257df1c41d0957dc9a5edffae05d95c1ab4b75b046af","schema_version":"1.0","event_id":"sha256:254bf93a3c054f1773a6257df1c41d0957dc9a5edffae05d95c1ab4b75b046af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6ARYZVYUKKUSGIT6YTE36YB5HE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The geodesic X-ray transform with a $GL(n,\\mathbb{C})$-connection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Fran\\c{c}ois Monard, Gabriel P. Paternain","submitted_at":"2016-10-29T21:33:13Z","abstract_excerpt":"We derive reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of such all transforms in a neighbourhood of constant curvature metrics and non-unitary connections with curvature close to zero. If certain Fredholm equations are injective in the absence of connection, then for any smooth enough connection multiplied by a complex parameter, the corresponding transform is injective for all values of that parameter outside a discrete set. Range characterizations are also provided, as well as numeric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09571","kind":"arxiv","version":2},"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":"2026-05-18T00:34:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MrKsYprVYqEudH+yTp7SsqvGW2/PZ9bZPkjpvZyMFW//863IUuxqMbvMt9s5ffg/TKTEVCnWyBgdtObtp9YCAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T16:03:51.747562Z"},"content_sha256":"44c915f3ecbfd5349edc4e11494e4609ef2636d41e46ec9cd96fc80e2bf32258","schema_version":"1.0","event_id":"sha256:44c915f3ecbfd5349edc4e11494e4609ef2636d41e46ec9cd96fc80e2bf32258"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ARYZVYUKKUSGIT6YTE36YB5HE/bundle.json","state_url":"https://pith.science/pith/6ARYZVYUKKUSGIT6YTE36YB5HE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ARYZVYUKKUSGIT6YTE36YB5HE/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":"2026-06-25T16:03:51Z","links":{"resolver":"https://pith.science/pith/6ARYZVYUKKUSGIT6YTE36YB5HE","bundle":"https://pith.science/pith/6ARYZVYUKKUSGIT6YTE36YB5HE/bundle.json","state":"https://pith.science/pith/6ARYZVYUKKUSGIT6YTE36YB5HE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ARYZVYUKKUSGIT6YTE36YB5HE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6ARYZVYUKKUSGIT6YTE36YB5HE","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":"9789599292bde8ac0a5006d81ef2c50f7298eb506bd5ee086e10639b9214e600","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-29T21:33:13Z","title_canon_sha256":"597f34128ff1cf6e70cd44df9e671c94ba522be9a14b33150849aa617face044"},"schema_version":"1.0","source":{"id":"1610.09571","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09571","created_at":"2026-05-18T00:34:39Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09571v2","created_at":"2026-05-18T00:34:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09571","created_at":"2026-05-18T00:34:39Z"},{"alias_kind":"pith_short_12","alias_value":"6ARYZVYUKKUS","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6ARYZVYUKKUSGIT6","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6ARYZVYU","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:44c915f3ecbfd5349edc4e11494e4609ef2636d41e46ec9cd96fc80e2bf32258","target":"graph","created_at":"2026-05-18T00:34:39Z","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 reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of such all transforms in a neighbourhood of constant curvature metrics and non-unitary connections with curvature close to zero. If certain Fredholm equations are injective in the absence of connection, then for any smooth enough connection multiplied by a complex parameter, the corresponding transform is injective for all values of that parameter outside a discrete set. Range characterizations are also provided, as well as numeric","authors_text":"Fran\\c{c}ois Monard, Gabriel P. Paternain","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-29T21:33:13Z","title":"The geodesic X-ray transform with a $GL(n,\\mathbb{C})$-connection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09571","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":"sha256:254bf93a3c054f1773a6257df1c41d0957dc9a5edffae05d95c1ab4b75b046af","target":"record","created_at":"2026-05-18T00:34:39Z","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":"9789599292bde8ac0a5006d81ef2c50f7298eb506bd5ee086e10639b9214e600","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-29T21:33:13Z","title_canon_sha256":"597f34128ff1cf6e70cd44df9e671c94ba522be9a14b33150849aa617face044"},"schema_version":"1.0","source":{"id":"1610.09571","kind":"arxiv","version":2}},"canonical_sha256":"f0238cd71452a923227ec4c9bf603d391f3a4bc7c0283b76de54c90ce1c833a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0238cd71452a923227ec4c9bf603d391f3a4bc7c0283b76de54c90ce1c833a6","first_computed_at":"2026-05-18T00:34:39.247534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:39.247534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CGWliC6wSI8mWu3nczAQdQdl8AfE/oRMPEvcDtsr7uogUtR9xKn1mcby70m67e1Yo+F1s+2BuJQGPnik7Ge4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:39.248070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09571","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:254bf93a3c054f1773a6257df1c41d0957dc9a5edffae05d95c1ab4b75b046af","sha256:44c915f3ecbfd5349edc4e11494e4609ef2636d41e46ec9cd96fc80e2bf32258"],"state_sha256":"65f0e1391e6869bf7e57e1a58cd43f6a6acefe3bed1b7c6201e2da6c1d67d597"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pzbS2DvpEZqNzgMkgWrZbDXy5B58DfnLVMh+8wzo5JlKL/D/S1FAmb+zU41ZsKboqaFTqkItPPXRYMol0YCiAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T16:03:51.749533Z","bundle_sha256":"93d79be9b501cf53ab216a8c11af39f48a00096256584dba166066f63f37f82b"}}