{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:J65UW4JJVFYVGHMJ2YSXLG6ZUM","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":"80532afa7d46ed8ebe9109fb22b8f1d68a1c817ce476f433da58f96da1675664","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-22T04:14:58Z","title_canon_sha256":"bfe02e65fde9214e591464f80bc92a89894b6e402fcf39d967b002ff991e1b95"},"schema_version":"1.0","source":{"id":"1709.07878","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.07878","created_at":"2026-05-18T00:34:28Z"},{"alias_kind":"arxiv_version","alias_value":"1709.07878v1","created_at":"2026-05-18T00:34:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.07878","created_at":"2026-05-18T00:34:28Z"},{"alias_kind":"pith_short_12","alias_value":"J65UW4JJVFYV","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"J65UW4JJVFYVGHMJ","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"J65UW4JJ","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:74f7e0198cae1505f24213394d96cb54732f384a7924bb2d754a5c500d29041b","target":"graph","created_at":"2026-05-18T00:34:28Z","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. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field pattern generated by one plane wave as the incident field. Based on our previous work (J. Comput. Phys. 345 (2017), 58-73), the translation invariance property of the phaseless far-field pattern can be broken by using infinitely many sets of superpositions of two plane waves as the incident fields at a fixed frequency. In this paper, we prove that the obstac","authors_text":"Bo Zhang, Haiwen Zhang, Xiaoxu Xu","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-22T04:14:58Z","title":"Uniqueness in inverse scattering problems with phaseless far-field data at a fixed frequency"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07878","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":"sha256:79f6bdde88bf37f88cd132aa1786b467e69c693d225b4f573923e5a8542ef244","target":"record","created_at":"2026-05-18T00:34:28Z","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":"80532afa7d46ed8ebe9109fb22b8f1d68a1c817ce476f433da58f96da1675664","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-22T04:14:58Z","title_canon_sha256":"bfe02e65fde9214e591464f80bc92a89894b6e402fcf39d967b002ff991e1b95"},"schema_version":"1.0","source":{"id":"1709.07878","kind":"arxiv","version":1}},"canonical_sha256":"4fbb4b7129a971531d89d625759bd9a33dd7b6d6031bbc1d56e1e3fb08cf21f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fbb4b7129a971531d89d625759bd9a33dd7b6d6031bbc1d56e1e3fb08cf21f5","first_computed_at":"2026-05-18T00:34:28.625762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:28.625762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s2WHE3cCDiIvw/KhweK46zU32qH/3bhhSx39M8kkh63186zGlpVT1LgU15XOi1dTFWtDHMb+mAj+rWQ7FErvCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:28.626179Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.07878","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79f6bdde88bf37f88cd132aa1786b467e69c693d225b4f573923e5a8542ef244","sha256:74f7e0198cae1505f24213394d96cb54732f384a7924bb2d754a5c500d29041b"],"state_sha256":"05cc2b2e6678c04b73cf167880cc1aed404b010eaa266e78d4ca901a6ea6f941"}