{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:KT7F3M3SNUXU24H2TVBZ2XT5QU","short_pith_number":"pith:KT7F3M3S","schema_version":"1.0","canonical_sha256":"54fe5db3726d2f4d70fa9d439d5e7d85176b1df9043bbf36e98785fb322413c8","source":{"kind":"arxiv","id":"1403.5984","version":2},"attestation_state":"computed","paper":{"title":"On the Role of Symmetries in the Theory of Photonic Crystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.optics"],"primary_cat":"cond-mat.mes-hall","authors_text":"Giuseppe De Nittis, Max Lein","submitted_at":"2014-03-24T14:55:11Z","abstract_excerpt":"We discuss the role of the symmetries in photonic crystals and classify them according to the Cartan-Altland-Zirnbauer scheme. Of particular importance are complex conjugation C and time-reversal T, but we identify also other significant symmetries. Borrowing the jargon of the classification theory of topological insulators, we show that C is a particle-hole-type symmetry rather than a time-reversal symmetry if one consider the Maxwell operator in the first-order formalism where the dynamical Maxwell equations can be rewritten as a Schr\\\"odinger equation; The symmetry which implements physical"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1403.5984","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2014-03-24T14:55:11Z","cross_cats_sorted":["math-ph","math.MP","physics.optics"],"title_canon_sha256":"e7d21a8ad277b73cba7a9810e606aeb4020a071c0699cbd845a47006a3158ee1","abstract_canon_sha256":"f025772d3a692bdce47324c0738269646a19736d306faeedc30b111abfbdee5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:28.724695Z","signature_b64":"ctsbJ4DlEYcKOZioaVdmh+nsGkI40ywltlGu1QbbqiigKJHEvhUgaWWxyzH+FGf8e2CuMa60nnboEuj2OpViAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54fe5db3726d2f4d70fa9d439d5e7d85176b1df9043bbf36e98785fb322413c8","last_reissued_at":"2026-05-18T02:24:28.723914Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:28.723914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Role of Symmetries in the Theory of Photonic Crystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.optics"],"primary_cat":"cond-mat.mes-hall","authors_text":"Giuseppe De Nittis, Max Lein","submitted_at":"2014-03-24T14:55:11Z","abstract_excerpt":"We discuss the role of the symmetries in photonic crystals and classify them according to the Cartan-Altland-Zirnbauer scheme. Of particular importance are complex conjugation C and time-reversal T, but we identify also other significant symmetries. Borrowing the jargon of the classification theory of topological insulators, we show that C is a particle-hole-type symmetry rather than a time-reversal symmetry if one consider the Maxwell operator in the first-order formalism where the dynamical Maxwell equations can be rewritten as a Schr\\\"odinger equation; The symmetry which implements physical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5984","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1403.5984","created_at":"2026-05-18T02:24:28.724038+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.5984v2","created_at":"2026-05-18T02:24:28.724038+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5984","created_at":"2026-05-18T02:24:28.724038+00:00"},{"alias_kind":"pith_short_12","alias_value":"KT7F3M3SNUXU","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KT7F3M3SNUXU24H2","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KT7F3M3S","created_at":"2026-05-18T12:28:35.611951+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KT7F3M3SNUXU24H2TVBZ2XT5QU","json":"https://pith.science/pith/KT7F3M3SNUXU24H2TVBZ2XT5QU.json","graph_json":"https://pith.science/api/pith-number/KT7F3M3SNUXU24H2TVBZ2XT5QU/graph.json","events_json":"https://pith.science/api/pith-number/KT7F3M3SNUXU24H2TVBZ2XT5QU/events.json","paper":"https://pith.science/paper/KT7F3M3S"},"agent_actions":{"view_html":"https://pith.science/pith/KT7F3M3SNUXU24H2TVBZ2XT5QU","download_json":"https://pith.science/pith/KT7F3M3SNUXU24H2TVBZ2XT5QU.json","view_paper":"https://pith.science/paper/KT7F3M3S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.5984&json=true","fetch_graph":"https://pith.science/api/pith-number/KT7F3M3SNUXU24H2TVBZ2XT5QU/graph.json","fetch_events":"https://pith.science/api/pith-number/KT7F3M3SNUXU24H2TVBZ2XT5QU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KT7F3M3SNUXU24H2TVBZ2XT5QU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KT7F3M3SNUXU24H2TVBZ2XT5QU/action/storage_attestation","attest_author":"https://pith.science/pith/KT7F3M3SNUXU24H2TVBZ2XT5QU/action/author_attestation","sign_citation":"https://pith.science/pith/KT7F3M3SNUXU24H2TVBZ2XT5QU/action/citation_signature","submit_replication":"https://pith.science/pith/KT7F3M3SNUXU24H2TVBZ2XT5QU/action/replication_record"}},"created_at":"2026-05-18T02:24:28.724038+00:00","updated_at":"2026-05-18T02:24:28.724038+00:00"}