{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2E5BKY4FXZARSZ4HPIVBSBH2GA","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":"f69ca5004fa2bb3452e1c8cff36d6ba5129216f15939bad3e857776ef746e9d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-24T11:07:54Z","title_canon_sha256":"27d818bec731c8d64b58112223d6a5869e4ba0f963631f6017997fcf50f316a9"},"schema_version":"1.0","source":{"id":"1806.09127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.09127","created_at":"2026-05-18T00:12:30Z"},{"alias_kind":"arxiv_version","alias_value":"1806.09127v1","created_at":"2026-05-18T00:12:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09127","created_at":"2026-05-18T00:12:30Z"},{"alias_kind":"pith_short_12","alias_value":"2E5BKY4FXZAR","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2E5BKY4FXZARSZ4H","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2E5BKY4F","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:86eecc2befedcc98a800dae52c34e5d33c74a360aa43368923a95df651c6153b","target":"graph","created_at":"2026-05-18T00:12:30Z","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":"This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. In our previous work ({\\em SIAM J. Appl. Math. \\bf78} (2018), 1737-1753), by utilizing spectral properties of the far-field operator we proved for the first time that the obstacle and the index of refraction of an inhomogeneous medium can be uniquely determined by the phaseless far-field patterns generated by infinitely many sets of superpositions of two plane waves with different directions at a fixed frequency under the a priori assumption that the obstacle is known to b","authors_text":"Bo Zhang, Haiwen Zhang, Xiaoxu Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-24T11:07:54Z","title":"Uniqueness in inverse scattering problems with phaseless far-field data at a fixed frequency. II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09127","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":"sha256:220d0465cc140ee81889cc4f1f980805434ee5a3f590ed06a8c03d3cb95c5806","target":"record","created_at":"2026-05-18T00:12:30Z","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":"f69ca5004fa2bb3452e1c8cff36d6ba5129216f15939bad3e857776ef746e9d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-24T11:07:54Z","title_canon_sha256":"27d818bec731c8d64b58112223d6a5869e4ba0f963631f6017997fcf50f316a9"},"schema_version":"1.0","source":{"id":"1806.09127","kind":"arxiv","version":1}},"canonical_sha256":"d13a156385be411967877a2a1904fa302d46849e41cbdf9a6f3d1cca282347ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d13a156385be411967877a2a1904fa302d46849e41cbdf9a6f3d1cca282347ac","first_computed_at":"2026-05-18T00:12:30.207887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:30.207887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2gu6z0cAey2FUiG3Z2ta+jYcllrP0+K6VdmF1FSGOlZjvVrB+TwSAgYZh5A1Qhvy1bEbeo6U7SSPDGiMSzh/CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:30.208484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.09127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:220d0465cc140ee81889cc4f1f980805434ee5a3f590ed06a8c03d3cb95c5806","sha256:86eecc2befedcc98a800dae52c34e5d33c74a360aa43368923a95df651c6153b"],"state_sha256":"1d7c65e2105c0d1f3e83bee679cd349dcf9db60c2ed52ff32828101e29f721c1"}