{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TCAWYX5CFT5AGYBOGQ7NLGZTK3","short_pith_number":"pith:TCAWYX5C","canonical_record":{"source":{"id":"1507.07827","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-28T16:04:56Z","cross_cats_sorted":[],"title_canon_sha256":"29543aefaeacb28f7dfb64f8d878f37bf135884778dc08440237603f74d27c0d","abstract_canon_sha256":"9fc71a28ce7742c01be4255a547440f490d4fd176803efdddaf9a0ff235e03fc"},"schema_version":"1.0"},"canonical_sha256":"98816c5fa22cfa03602e343ed59b3356f42703804c963cfa8e2e59789c0c1c56","source":{"kind":"arxiv","id":"1507.07827","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07827","created_at":"2026-05-18T01:22:37Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07827v2","created_at":"2026-05-18T01:22:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07827","created_at":"2026-05-18T01:22:37Z"},{"alias_kind":"pith_short_12","alias_value":"TCAWYX5CFT5A","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TCAWYX5CFT5AGYBO","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TCAWYX5C","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TCAWYX5CFT5AGYBOGQ7NLGZTK3","target":"record","payload":{"canonical_record":{"source":{"id":"1507.07827","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-28T16:04:56Z","cross_cats_sorted":[],"title_canon_sha256":"29543aefaeacb28f7dfb64f8d878f37bf135884778dc08440237603f74d27c0d","abstract_canon_sha256":"9fc71a28ce7742c01be4255a547440f490d4fd176803efdddaf9a0ff235e03fc"},"schema_version":"1.0"},"canonical_sha256":"98816c5fa22cfa03602e343ed59b3356f42703804c963cfa8e2e59789c0c1c56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:37.565709Z","signature_b64":"dzBd1/IpzXpsMs/dusA05fIbomqhHeubfQExTQxcL5/ime/YS9e410q5ZsnscLLUi6rC6oYl2XF1m2UxSVgIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98816c5fa22cfa03602e343ed59b3356f42703804c963cfa8e2e59789c0c1c56","last_reissued_at":"2026-05-18T01:22:37.565120Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:37.565120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.07827","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":"2026-05-18T01:22:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/w9sWzr7Yr/be+rE02G3IaC4MBtfl2QZ2mwkB1zJQM7iTQ03Nqgm3sll4t47wW7Sx4O2ITDx2OlVfE8hySJNCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:50:44.075731Z"},"content_sha256":"88334e2d64255877bee901035082e59eba1f070dcbe8618d3915732fc378a443","schema_version":"1.0","event_id":"sha256:88334e2d64255877bee901035082e59eba1f070dcbe8618d3915732fc378a443"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TCAWYX5CFT5AGYBOGQ7NLGZTK3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical approximation of the potential in the two-dimensional inverse scattering problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Carlos Castro, Juan Antonio Barcel\\'o, Juan Manuel Reyes","submitted_at":"2015-07-28T16:04:56Z","abstract_excerpt":"We present an iterative algorithm to compute numerical approximations of the potential for the Schr\\\"odinger operator from scattering data. Four different types of scattering data are used as follows: fixed energy, fixed incident angle, backscattering and full data. In the case of fixed energy, the algorithm coincides basically with the one recently introduced by Novikov in [Novikov, R. G., \"An iterative approach to non-overdetermined inverse scattering at fixed energy\", Sbornik: Mathematics 206 (1), 120-134 (2015)], where some estimates are obtained for large energy scattering data. The numer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07827","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":"2026-05-18T01:22:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KFSYEkFmbLrX8pQe9utlLPczkQ1LoDYN4N7e2IvsY+SGTPmFZNVnxRODbaZ2lpK4ZwQy2ZXsRXQxRl92oFmJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:50:44.076205Z"},"content_sha256":"851af9254deca4299d1d3ec18f6ff37e2d349252fc60836486ee5fe7101c29cd","schema_version":"1.0","event_id":"sha256:851af9254deca4299d1d3ec18f6ff37e2d349252fc60836486ee5fe7101c29cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TCAWYX5CFT5AGYBOGQ7NLGZTK3/bundle.json","state_url":"https://pith.science/pith/TCAWYX5CFT5AGYBOGQ7NLGZTK3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TCAWYX5CFT5AGYBOGQ7NLGZTK3/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":"2026-05-28T12:50:44Z","links":{"resolver":"https://pith.science/pith/TCAWYX5CFT5AGYBOGQ7NLGZTK3","bundle":"https://pith.science/pith/TCAWYX5CFT5AGYBOGQ7NLGZTK3/bundle.json","state":"https://pith.science/pith/TCAWYX5CFT5AGYBOGQ7NLGZTK3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TCAWYX5CFT5AGYBOGQ7NLGZTK3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TCAWYX5CFT5AGYBOGQ7NLGZTK3","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":"9fc71a28ce7742c01be4255a547440f490d4fd176803efdddaf9a0ff235e03fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-28T16:04:56Z","title_canon_sha256":"29543aefaeacb28f7dfb64f8d878f37bf135884778dc08440237603f74d27c0d"},"schema_version":"1.0","source":{"id":"1507.07827","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07827","created_at":"2026-05-18T01:22:37Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07827v2","created_at":"2026-05-18T01:22:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07827","created_at":"2026-05-18T01:22:37Z"},{"alias_kind":"pith_short_12","alias_value":"TCAWYX5CFT5A","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TCAWYX5CFT5AGYBO","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TCAWYX5C","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:851af9254deca4299d1d3ec18f6ff37e2d349252fc60836486ee5fe7101c29cd","target":"graph","created_at":"2026-05-18T01:22:37Z","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 present an iterative algorithm to compute numerical approximations of the potential for the Schr\\\"odinger operator from scattering data. Four different types of scattering data are used as follows: fixed energy, fixed incident angle, backscattering and full data. In the case of fixed energy, the algorithm coincides basically with the one recently introduced by Novikov in [Novikov, R. G., \"An iterative approach to non-overdetermined inverse scattering at fixed energy\", Sbornik: Mathematics 206 (1), 120-134 (2015)], where some estimates are obtained for large energy scattering data. The numer","authors_text":"Carlos Castro, Juan Antonio Barcel\\'o, Juan Manuel Reyes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-28T16:04:56Z","title":"Numerical approximation of the potential in the two-dimensional inverse scattering problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07827","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":"sha256:88334e2d64255877bee901035082e59eba1f070dcbe8618d3915732fc378a443","target":"record","created_at":"2026-05-18T01:22:37Z","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":"9fc71a28ce7742c01be4255a547440f490d4fd176803efdddaf9a0ff235e03fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-28T16:04:56Z","title_canon_sha256":"29543aefaeacb28f7dfb64f8d878f37bf135884778dc08440237603f74d27c0d"},"schema_version":"1.0","source":{"id":"1507.07827","kind":"arxiv","version":2}},"canonical_sha256":"98816c5fa22cfa03602e343ed59b3356f42703804c963cfa8e2e59789c0c1c56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98816c5fa22cfa03602e343ed59b3356f42703804c963cfa8e2e59789c0c1c56","first_computed_at":"2026-05-18T01:22:37.565120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:37.565120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dzBd1/IpzXpsMs/dusA05fIbomqhHeubfQExTQxcL5/ime/YS9e410q5ZsnscLLUi6rC6oYl2XF1m2UxSVgIAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:37.565709Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.07827","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88334e2d64255877bee901035082e59eba1f070dcbe8618d3915732fc378a443","sha256:851af9254deca4299d1d3ec18f6ff37e2d349252fc60836486ee5fe7101c29cd"],"state_sha256":"12e9349bbcca0d1ebda867d19d0e652ad8cf0d003289108d02abed7617df8830"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y8Uaf/7WlQOrgE2NyLZKdTJYUPcKVrNy+ZTjpZubiSTMxQhyYFBTRBrCisKngt3XhSiQK1Flt65WdQgJJH1rBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:50:44.078536Z","bundle_sha256":"559195b282400b2c2954b9080f16fd7e104e15ef4a559dfb23323c0bef310817"}}