{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NYKIWUCDDI5JVH6VY62IXFU6WQ","short_pith_number":"pith:NYKIWUCD","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"},"canonical_sha256":"6e148b50431a3a9a9fd5c7b48b969eb4140aa7cdfbe0bbb6e63ccbf716ad8ce1","source":{"kind":"arxiv","id":"1202.3583","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3583","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3583v1","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3583","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"pith_short_12","alias_value":"NYKIWUCDDI5J","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NYKIWUCDDI5JVH6V","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NYKIWUCD","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NYKIWUCDDI5JVH6VY62IXFU6WQ","target":"record","payload":{"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"},"canonical_sha256":"6e148b50431a3a9a9fd5c7b48b969eb4140aa7cdfbe0bbb6e63ccbf716ad8ce1","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"},"source_kind":"arxiv","source_id":"1202.3583","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:02:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"osNKb0OZgeYXufLlnJ9xwopCGZBdvJgHEQpxzPCi6XPR8/qsD6TrXz/uPXOjZ6St1DSW87jnew8n4hRElR4aAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:17:40.016480Z"},"content_sha256":"c76692003f2522850ba32176529e77c22e7e3ea9a837fca7bcb561d4d481829b","schema_version":"1.0","event_id":"sha256:c76692003f2522850ba32176529e77c22e7e3ea9a837fca7bcb561d4d481829b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NYKIWUCDDI5JVH6VY62IXFU6WQ","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:02:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C6LJm1MPUdw2q3l2UXQoxJW3DP4uq/U0VanISaKU43in2bxQbcdvBS/7y26yhTH0u4vcM91zPv2VkXPe9nXFBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:17:40.017159Z"},"content_sha256":"a26231921503d008e9169631ad6887244f8e0ba7ace21f11a3cc2be824a495f5","schema_version":"1.0","event_id":"sha256:a26231921503d008e9169631ad6887244f8e0ba7ace21f11a3cc2be824a495f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NYKIWUCDDI5JVH6VY62IXFU6WQ/bundle.json","state_url":"https://pith.science/pith/NYKIWUCDDI5JVH6VY62IXFU6WQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NYKIWUCDDI5JVH6VY62IXFU6WQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T14:17:40Z","links":{"resolver":"https://pith.science/pith/NYKIWUCDDI5JVH6VY62IXFU6WQ","bundle":"https://pith.science/pith/NYKIWUCDDI5JVH6VY62IXFU6WQ/bundle.json","state":"https://pith.science/pith/NYKIWUCDDI5JVH6VY62IXFU6WQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NYKIWUCDDI5JVH6VY62IXFU6WQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NYKIWUCDDI5JVH6VY62IXFU6WQ","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":"fad0e227041237752970e634b81fc6c0eb84bfabb2e65e360cf8b1f8de6c333f","cross_cats_sorted":["math.AP","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-02-16T13:14:09Z","title_canon_sha256":"da0c7fcc1217a5f9e548c83f64e95f8757c432a94546eebfc96b4f736255b68e"},"schema_version":"1.0","source":{"id":"1202.3583","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3583","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3583v1","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3583","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"pith_short_12","alias_value":"NYKIWUCDDI5J","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NYKIWUCDDI5JVH6V","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NYKIWUCD","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:a26231921503d008e9169631ad6887244f8e0ba7ace21f11a3cc2be824a495f5","target":"graph","created_at":"2026-05-18T04:02:12Z","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":"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","authors_text":"Tomas Dohnal, Willy Doerfler","cross_cats":["math.AP","physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-02-16T13:14:09Z","title":"Coupled Mode Equation Modeling for Out-of-Plane Gap Solitons in 2D Photonic Crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3583","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:c76692003f2522850ba32176529e77c22e7e3ea9a837fca7bcb561d4d481829b","target":"record","created_at":"2026-05-18T04:02:12Z","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":"fad0e227041237752970e634b81fc6c0eb84bfabb2e65e360cf8b1f8de6c333f","cross_cats_sorted":["math.AP","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-02-16T13:14:09Z","title_canon_sha256":"da0c7fcc1217a5f9e548c83f64e95f8757c432a94546eebfc96b4f736255b68e"},"schema_version":"1.0","source":{"id":"1202.3583","kind":"arxiv","version":1}},"canonical_sha256":"6e148b50431a3a9a9fd5c7b48b969eb4140aa7cdfbe0bbb6e63ccbf716ad8ce1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e148b50431a3a9a9fd5c7b48b969eb4140aa7cdfbe0bbb6e63ccbf716ad8ce1","first_computed_at":"2026-05-18T04:02:12.826982Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:12.826982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"98oNdiQzhyp82FJ3gLhpteHYSds9JOwum1jca/Eb+xTGFwT8g1j3E2CZREcEHa+Y1HwLCNUwT6lnuNG+eroEAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:12.827576Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3583","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c76692003f2522850ba32176529e77c22e7e3ea9a837fca7bcb561d4d481829b","sha256:a26231921503d008e9169631ad6887244f8e0ba7ace21f11a3cc2be824a495f5"],"state_sha256":"6c5c3c6c9ba836889897f7ae7d564ef2c52d43bfbd45ba9089ec8f8a4c6f0b78"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q8+R2WmfMeQzfRoXxHK8DOXFsiYaemBF66kDS8xTrfm0QMA2U/d1d7crK86pWIPEyi5nmxViPd4cynDFx0mMCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T14:17:40.020634Z","bundle_sha256":"bf031726e846bed08e94752cd1ace74ce3f0bb25f18d6f0ff60c8b702b030844"}}