{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Y2COD5DUMZN76DW2HBLWBTGGCL","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":"d1871d5aa8dd73ffa4a27b17242f297f5c0e85ad7cfef6b6ca9570b30ed5d3a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2016-01-21T01:54:14Z","title_canon_sha256":"c16d4717f7a0c5aa5d05de5d1d1b9e2ced2c72079bd2658552812fe1cbaedd96"},"schema_version":"1.0","source":{"id":"1601.05489","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05489","created_at":"2026-05-18T01:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05489v1","created_at":"2026-05-18T01:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05489","created_at":"2026-05-18T01:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"Y2COD5DUMZN7","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"Y2COD5DUMZN76DW2","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"Y2COD5DU","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:8dd4ff3d2fc2009f02283a712e62ba019c6b5e6de8a81a6f6e8ad726118f7508","target":"graph","created_at":"2026-05-18T01:13:56Z","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 investigate the properties of multidimensional parity-time symmetric periodic systems whose non-Hermitian periodicity is an integer multiple of the underlying Hermitian system's periodicity. This creates a natural set of degeneracies which can undergo thresholdless $\\mathcal{PT}$ transitions. We derive a $\\mathbf{k} \\cdot \\mathbf{p}$ perturbation theory suited to the continuous eigenvalues of such systems in terms of the modes of the underlying Hermitian system. In photonic crystals, such thresholdless $\\mathcal{PT}$ transitions are shown to yield significant control over the band structure","authors_text":"Aaswath Raman, Alexander Cerjan, Shanhui Fan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2016-01-21T01:54:14Z","title":"Exceptional contours and band structure design in parity-time symmetric photonic crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05489","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:dc64d6324987e5d4efe1dafe4d7b921d654a919b77e48f8c9f25db686464c2d2","target":"record","created_at":"2026-05-18T01:13:56Z","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":"d1871d5aa8dd73ffa4a27b17242f297f5c0e85ad7cfef6b6ca9570b30ed5d3a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2016-01-21T01:54:14Z","title_canon_sha256":"c16d4717f7a0c5aa5d05de5d1d1b9e2ced2c72079bd2658552812fe1cbaedd96"},"schema_version":"1.0","source":{"id":"1601.05489","kind":"arxiv","version":1}},"canonical_sha256":"c684e1f474665bff0eda385760ccc612f68d8ccddc6a64d19831d463339035a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c684e1f474665bff0eda385760ccc612f68d8ccddc6a64d19831d463339035a0","first_computed_at":"2026-05-18T01:13:56.237956Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:56.237956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NauhbuEyW/6CvVkGR6okemXwl/VNlvQCw3ZGyRxwbUoN2pZCeOPhZ9bvPh1UZH7OKQ2m0WY4cCVVwzs6ADjoDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:56.238420Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05489","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc64d6324987e5d4efe1dafe4d7b921d654a919b77e48f8c9f25db686464c2d2","sha256:8dd4ff3d2fc2009f02283a712e62ba019c6b5e6de8a81a6f6e8ad726118f7508"],"state_sha256":"005a3f64a7825d8837d13dde6bc77787337205bcc33e08da19306420d7c37fd1"}