{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:23DEZBHVZR7XCGQVJZ2PA3KYFT","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":"04a0f787e5f70b0f1447480060743afab0702615af5549e125e7a3eac7ccacea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-01-06T20:41:43Z","title_canon_sha256":"c11b0ad97c77d735902c26bcfbac23a9d8dc336fdcbf96cc4aefd55498b41f93"},"schema_version":"1.0","source":{"id":"1001.0962","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.0962","created_at":"2026-05-18T02:10:04Z"},{"alias_kind":"arxiv_version","alias_value":"1001.0962v1","created_at":"2026-05-18T02:10:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0962","created_at":"2026-05-18T02:10:04Z"},{"alias_kind":"pith_short_12","alias_value":"23DEZBHVZR7X","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"23DEZBHVZR7XCGQV","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"23DEZBHV","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:08eb141d8da2caf73260c00075ea7b8e7bb18182c1102844d45a0fe9bd2c56f6","target":"graph","created_at":"2026-05-18T02:10:04Z","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":"Spectral singularities that spoil the completeness of Bloch-Floquet states may occur in non-Hermitian Hamiltonians with complex periodic potentials. Here an equivalence is established between spectral singularities in complex crystals and secularities that arise in Bragg diffraction patterns. Signatures of spectral singularities in a scattering process with wave packets are elucidated for a PT-symmetric complex crystal.","authors_text":"S. Longhi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-01-06T20:41:43Z","title":"Spectral singularities and Bragg scattering in complex crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0962","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":"sha256:9eb76838dd47268ea6d871b6f7d7a38a8f72fe0da7e1e0975a48fdcfd43a29b5","target":"record","created_at":"2026-05-18T02:10:04Z","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":"04a0f787e5f70b0f1447480060743afab0702615af5549e125e7a3eac7ccacea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-01-06T20:41:43Z","title_canon_sha256":"c11b0ad97c77d735902c26bcfbac23a9d8dc336fdcbf96cc4aefd55498b41f93"},"schema_version":"1.0","source":{"id":"1001.0962","kind":"arxiv","version":1}},"canonical_sha256":"d6c64c84f5cc7f711a154e74f06d582ccfe6ecef7146b8551649e43edba51a4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6c64c84f5cc7f711a154e74f06d582ccfe6ecef7146b8551649e43edba51a4b","first_computed_at":"2026-05-18T02:10:04.368124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:10:04.368124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EICN29ndjCMSlBVck1uUwDMekdQ08YH2a2Ri30eIs24MyiceLOPWDzgUvQT1Mv+85Vwu3ntEczMOHPzM4IbWCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:10:04.368894Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.0962","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9eb76838dd47268ea6d871b6f7d7a38a8f72fe0da7e1e0975a48fdcfd43a29b5","sha256:08eb141d8da2caf73260c00075ea7b8e7bb18182c1102844d45a0fe9bd2c56f6"],"state_sha256":"2c4fec4d75ec1bee52002b01e63b7fdc1afa6f9e41b217775b7f37571bd14b00"}