{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:NYKIWUCDDI5JVH6VY62IXFU6WQ","short_pith_number":"pith:NYKIWUCD","schema_version":"1.0","canonical_sha256":"6e148b50431a3a9a9fd5c7b48b969eb4140aa7cdfbe0bbb6e63ccbf716ad8ce1","source":{"kind":"arxiv","id":"1202.3583","version":1},"attestation_state":"computed","paper":{"title":"Coupled Mode Equation Modeling for Out-of-Plane Gap Solitons in 2D Photonic Crystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","physics.optics"],"primary_cat":"nlin.PS","authors_text":"Tomas Dohnal, Willy Doerfler","submitted_at":"2012-02-16T13:14:09Z","abstract_excerpt":"Out-of-plane gap solitons in 2D photonic crystals are optical beams localized in the plane of periodicity of the medium and delocalized in the orthogonal direction, in which they propagate with a nonzero velocity. We study such gap solitons as described by the Kerr nonlinear Maxwell system. Using a model of the nonlinear polarization, which does not generate higher harmonics, we obtain a closed curl-curl problem for the fundamental harmonic of the gap soliton. For gap solitons with frequencies inside spectral gaps and in an asymptotic vicinity of a gap edge we use a slowly varying envelope app"},"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":"1202.3583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-02-16T13:14:09Z","cross_cats_sorted":["math.AP","physics.optics"],"title_canon_sha256":"da0c7fcc1217a5f9e548c83f64e95f8757c432a94546eebfc96b4f736255b68e","abstract_canon_sha256":"fad0e227041237752970e634b81fc6c0eb84bfabb2e65e360cf8b1f8de6c333f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:12.827576Z","signature_b64":"98oNdiQzhyp82FJ3gLhpteHYSds9JOwum1jca/Eb+xTGFwT8g1j3E2CZREcEHa+Y1HwLCNUwT6lnuNG+eroEAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e148b50431a3a9a9fd5c7b48b969eb4140aa7cdfbe0bbb6e63ccbf716ad8ce1","last_reissued_at":"2026-05-18T04:02:12.826982Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:12.826982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coupled Mode Equation Modeling for Out-of-Plane Gap Solitons in 2D Photonic Crystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","physics.optics"],"primary_cat":"nlin.PS","authors_text":"Tomas Dohnal, Willy Doerfler","submitted_at":"2012-02-16T13:14:09Z","abstract_excerpt":"Out-of-plane gap solitons in 2D photonic crystals are optical beams localized in the plane of periodicity of the medium and delocalized in the orthogonal direction, in which they propagate with a nonzero velocity. We study such gap solitons as described by the Kerr nonlinear Maxwell system. Using a model of the nonlinear polarization, which does not generate higher harmonics, we obtain a closed curl-curl problem for the fundamental harmonic of the gap soliton. For gap solitons with frequencies inside spectral gaps and in an asymptotic vicinity of a gap edge we use a slowly varying envelope app"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3583","kind":"arxiv","version":1},"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":"1202.3583","created_at":"2026-05-18T04:02:12.827073+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.3583v1","created_at":"2026-05-18T04:02:12.827073+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3583","created_at":"2026-05-18T04:02:12.827073+00:00"},{"alias_kind":"pith_short_12","alias_value":"NYKIWUCDDI5J","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"NYKIWUCDDI5JVH6V","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"NYKIWUCD","created_at":"2026-05-18T12:27:16.716162+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/NYKIWUCDDI5JVH6VY62IXFU6WQ","json":"https://pith.science/pith/NYKIWUCDDI5JVH6VY62IXFU6WQ.json","graph_json":"https://pith.science/api/pith-number/NYKIWUCDDI5JVH6VY62IXFU6WQ/graph.json","events_json":"https://pith.science/api/pith-number/NYKIWUCDDI5JVH6VY62IXFU6WQ/events.json","paper":"https://pith.science/paper/NYKIWUCD"},"agent_actions":{"view_html":"https://pith.science/pith/NYKIWUCDDI5JVH6VY62IXFU6WQ","download_json":"https://pith.science/pith/NYKIWUCDDI5JVH6VY62IXFU6WQ.json","view_paper":"https://pith.science/paper/NYKIWUCD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.3583&json=true","fetch_graph":"https://pith.science/api/pith-number/NYKIWUCDDI5JVH6VY62IXFU6WQ/graph.json","fetch_events":"https://pith.science/api/pith-number/NYKIWUCDDI5JVH6VY62IXFU6WQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NYKIWUCDDI5JVH6VY62IXFU6WQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NYKIWUCDDI5JVH6VY62IXFU6WQ/action/storage_attestation","attest_author":"https://pith.science/pith/NYKIWUCDDI5JVH6VY62IXFU6WQ/action/author_attestation","sign_citation":"https://pith.science/pith/NYKIWUCDDI5JVH6VY62IXFU6WQ/action/citation_signature","submit_replication":"https://pith.science/pith/NYKIWUCDDI5JVH6VY62IXFU6WQ/action/replication_record"}},"created_at":"2026-05-18T04:02:12.827073+00:00","updated_at":"2026-05-18T04:02:12.827073+00:00"}