{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VOWV4IL7J5CFVXTOSBTFBTPTYL","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":"757493b6274ff5ff91248dfc5a89aaa08c21ea6ab841b58f5dafc22d4009259c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-11T12:02:35Z","title_canon_sha256":"cc92249f3a2fea64e3cc53c4fc435ae8a4c4d9299806a5b35d2829f095ae8de0"},"schema_version":"1.0","source":{"id":"1210.3194","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3194","created_at":"2026-05-18T03:43:28Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3194v1","created_at":"2026-05-18T03:43:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3194","created_at":"2026-05-18T03:43:28Z"},{"alias_kind":"pith_short_12","alias_value":"VOWV4IL7J5CF","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VOWV4IL7J5CFVXTO","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VOWV4IL7","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:522bf7e87d1467380824bc4eec5ed027b673b6696ba1e6ea1436f81a536bf0a9","target":"graph","created_at":"2026-05-18T03:43:28Z","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":"In scattering theory the far field pattern describes the directional dependence of a time-harmonic wave scattered by an obstacle or inhomogeneous medium, when observed sufficiently far away from these objects. Considering plane wave excitations, the far field pattern can be written as a function of two variables, namely the direction of propagation of the incident plane wave and the observation direction, and it is well-known to be separately real analytic with respect to each of them. We show that the far field pattern is in fact a jointly real analytic function of these two variables.","authors_text":"Nuutti Hyv\\\"onen, Otto Seiskari, Roland Griesmaier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-11T12:02:35Z","title":"A note on analyticity properties of far field patterns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3194","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":"sha256:77e676068c78a28b80ae40c8cf0da5e2ea204e15bd835ba1309fc42097f01ea3","target":"record","created_at":"2026-05-18T03:43:28Z","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":"757493b6274ff5ff91248dfc5a89aaa08c21ea6ab841b58f5dafc22d4009259c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-11T12:02:35Z","title_canon_sha256":"cc92249f3a2fea64e3cc53c4fc435ae8a4c4d9299806a5b35d2829f095ae8de0"},"schema_version":"1.0","source":{"id":"1210.3194","kind":"arxiv","version":1}},"canonical_sha256":"abad5e217f4f445ade6e906650cdf3c2c20ee1204f92eac29389dacea29a33f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abad5e217f4f445ade6e906650cdf3c2c20ee1204f92eac29389dacea29a33f2","first_computed_at":"2026-05-18T03:43:28.076346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:28.076346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pz3wUSnqQhINdOlQjJUBitdGyYckER6xbpZ07n29F5y4ZGhoSPcDoWRZ8hh8dVH2GHeyXHvwe/qIJRobMd1OAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:28.076846Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3194","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77e676068c78a28b80ae40c8cf0da5e2ea204e15bd835ba1309fc42097f01ea3","sha256:522bf7e87d1467380824bc4eec5ed027b673b6696ba1e6ea1436f81a536bf0a9"],"state_sha256":"7d109c22aa2806219f3f094c7e313db6ecf27e77e5df1775531e9befc4ad0a19"}