{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:KTQNDF5BLHZI5BUPMYF3KPTP37","short_pith_number":"pith:KTQNDF5B","schema_version":"1.0","canonical_sha256":"54e0d197a159f28e868f660bb53e6fdffd287a56f14891a57d00dd645e36a7ac","source":{"kind":"arxiv","id":"0910.2742","version":2},"attestation_state":"computed","paper":{"title":"On the Bethe-Sommerfeld conjecture for periodic Maxwell operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Mariya Vorobets","submitted_at":"2009-10-14T22:28:44Z","abstract_excerpt":"The Bethe-Sommerfeld conjecture states that the spectrum of the stationary Schrodinger operator with a periodic potential in dimensions higher than 1 has only finitely many gaps. After work done by many authors, it has been proven by now in full generality. The similar conjecture in presence of a periodic magnetic potential has been proven in dimension 2 only. Another case of a significant interest, due to its importance for the photonic crystal theory, is of a periodic Maxwell operator, where apparently no results of such kind are known. We establish here that in the case of a 2D photonic cry"},"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":"0910.2742","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-10-14T22:28:44Z","cross_cats_sorted":[],"title_canon_sha256":"0cdb0eabae90e34c27c6df466f30848b0ec48191b07c59efb69f55f5906b9a84","abstract_canon_sha256":"0ef39e50cf15b6e5e77e7181af468e3a5e7225347b39ccb217bc16764ba93c57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:35.327614Z","signature_b64":"cHHVA9DyxqFZ3VA/FGYf+9S8r/c0vq77DTxS6BJ5bZoVPs9pY8hK++D4W3x2zbbe7q94BM1/fVXAh9OqMvLaBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54e0d197a159f28e868f660bb53e6fdffd287a56f14891a57d00dd645e36a7ac","last_reissued_at":"2026-05-18T04:42:35.326957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:35.326957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Bethe-Sommerfeld conjecture for periodic Maxwell operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Mariya Vorobets","submitted_at":"2009-10-14T22:28:44Z","abstract_excerpt":"The Bethe-Sommerfeld conjecture states that the spectrum of the stationary Schrodinger operator with a periodic potential in dimensions higher than 1 has only finitely many gaps. After work done by many authors, it has been proven by now in full generality. The similar conjecture in presence of a periodic magnetic potential has been proven in dimension 2 only. Another case of a significant interest, due to its importance for the photonic crystal theory, is of a periodic Maxwell operator, where apparently no results of such kind are known. We establish here that in the case of a 2D photonic cry"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2742","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":"0910.2742","created_at":"2026-05-18T04:42:35.327035+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.2742v2","created_at":"2026-05-18T04:42:35.327035+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2742","created_at":"2026-05-18T04:42:35.327035+00:00"},{"alias_kind":"pith_short_12","alias_value":"KTQNDF5BLHZI","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"KTQNDF5BLHZI5BUP","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"KTQNDF5B","created_at":"2026-05-18T12:26:00.592388+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/KTQNDF5BLHZI5BUPMYF3KPTP37","json":"https://pith.science/pith/KTQNDF5BLHZI5BUPMYF3KPTP37.json","graph_json":"https://pith.science/api/pith-number/KTQNDF5BLHZI5BUPMYF3KPTP37/graph.json","events_json":"https://pith.science/api/pith-number/KTQNDF5BLHZI5BUPMYF3KPTP37/events.json","paper":"https://pith.science/paper/KTQNDF5B"},"agent_actions":{"view_html":"https://pith.science/pith/KTQNDF5BLHZI5BUPMYF3KPTP37","download_json":"https://pith.science/pith/KTQNDF5BLHZI5BUPMYF3KPTP37.json","view_paper":"https://pith.science/paper/KTQNDF5B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.2742&json=true","fetch_graph":"https://pith.science/api/pith-number/KTQNDF5BLHZI5BUPMYF3KPTP37/graph.json","fetch_events":"https://pith.science/api/pith-number/KTQNDF5BLHZI5BUPMYF3KPTP37/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KTQNDF5BLHZI5BUPMYF3KPTP37/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KTQNDF5BLHZI5BUPMYF3KPTP37/action/storage_attestation","attest_author":"https://pith.science/pith/KTQNDF5BLHZI5BUPMYF3KPTP37/action/author_attestation","sign_citation":"https://pith.science/pith/KTQNDF5BLHZI5BUPMYF3KPTP37/action/citation_signature","submit_replication":"https://pith.science/pith/KTQNDF5BLHZI5BUPMYF3KPTP37/action/replication_record"}},"created_at":"2026-05-18T04:42:35.327035+00:00","updated_at":"2026-05-18T04:42:35.327035+00:00"}