{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CPEE2JNMLQZIMIPLHVQDKMGNN7","short_pith_number":"pith:CPEE2JNM","canonical_record":{"source":{"id":"1511.03723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-11T23:08:31Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"18df28346fd74adb37e340c53d3269a236a3389eb0b355be2b77ae8bd5ef87e2","abstract_canon_sha256":"d0321cb85d9f757faed5ff0493d5254c6e11ccc17535d72628e47942e46c0448"},"schema_version":"1.0"},"canonical_sha256":"13c84d25ac5c328621eb3d603530cd6fd593734da4e417039177f1933a144bd2","source":{"kind":"arxiv","id":"1511.03723","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03723","created_at":"2026-05-18T00:45:08Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03723v1","created_at":"2026-05-18T00:45:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03723","created_at":"2026-05-18T00:45:08Z"},{"alias_kind":"pith_short_12","alias_value":"CPEE2JNMLQZI","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CPEE2JNMLQZIMIPL","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CPEE2JNM","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CPEE2JNMLQZIMIPLHVQDKMGNN7","target":"record","payload":{"canonical_record":{"source":{"id":"1511.03723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-11T23:08:31Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"18df28346fd74adb37e340c53d3269a236a3389eb0b355be2b77ae8bd5ef87e2","abstract_canon_sha256":"d0321cb85d9f757faed5ff0493d5254c6e11ccc17535d72628e47942e46c0448"},"schema_version":"1.0"},"canonical_sha256":"13c84d25ac5c328621eb3d603530cd6fd593734da4e417039177f1933a144bd2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:08.539667Z","signature_b64":"lwvHfBCeBH93xUFJdMTnkLeAxpo7gmWzvyzptpy0krBQoHhbYMJ9GamEU/tSoCGslC/uvD4sI0rfzU8aDBRxDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13c84d25ac5c328621eb3d603530cd6fd593734da4e417039177f1933a144bd2","last_reissued_at":"2026-05-18T00:45:08.538968Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:08.538968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.03723","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":"2026-05-18T00:45:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JnUcWnvSWdPvfOeBbMnGpOgqrGS1aB9b4pPFAgOdR0KUACX0RX/EKA/s9vliq8FcBk5ljmmJFds8vGGaVst6Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:46:44.804090Z"},"content_sha256":"c4ad3c5ccf9ef5ab4d1a0a44e0c3e9263dc75e076321be0fa5175f1b85e59ad5","schema_version":"1.0","event_id":"sha256:c4ad3c5ccf9ef5ab4d1a0a44e0c3e9263dc75e076321be0fa5175f1b85e59ad5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CPEE2JNMLQZIMIPLHVQDKMGNN7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gap localization of TE-Modes by arbitrarily weak defects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Ian Wood, Malcolm Brown, Maria Radosz, Michael Plum, Vu Hoang","submitted_at":"2015-11-11T23:08:31Z","abstract_excerpt":"This paper considers the propagation of TE-modes in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a periodic background medium. Both the periodic background problem and the perturbed problem are modelled by a divergence type equation. A feature of our analysis is that we allow discontinuities in the coefficients of the operator, which is required to model many photonic crystals. It is shown that arbitrarily weak perturbations introduce spectrum into the spectral gaps of the background operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03723","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":"2026-05-18T00:45:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mh9Mt8B3nLCHk1DbELx+VyMmfdm8HW3TUAvnvjx9nDCN/usPH2NEHvNnHFtueKeTgQUbH3tY1P0zhCEr8c7+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:46:44.804819Z"},"content_sha256":"5e2757dcc07b7c6ebc006a8d968d76b3c25f1ec0b1ec571497074c361e40bd5c","schema_version":"1.0","event_id":"sha256:5e2757dcc07b7c6ebc006a8d968d76b3c25f1ec0b1ec571497074c361e40bd5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CPEE2JNMLQZIMIPLHVQDKMGNN7/bundle.json","state_url":"https://pith.science/pith/CPEE2JNMLQZIMIPLHVQDKMGNN7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CPEE2JNMLQZIMIPLHVQDKMGNN7/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":"2026-05-31T19:46:44Z","links":{"resolver":"https://pith.science/pith/CPEE2JNMLQZIMIPLHVQDKMGNN7","bundle":"https://pith.science/pith/CPEE2JNMLQZIMIPLHVQDKMGNN7/bundle.json","state":"https://pith.science/pith/CPEE2JNMLQZIMIPLHVQDKMGNN7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CPEE2JNMLQZIMIPLHVQDKMGNN7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CPEE2JNMLQZIMIPLHVQDKMGNN7","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":"d0321cb85d9f757faed5ff0493d5254c6e11ccc17535d72628e47942e46c0448","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-11T23:08:31Z","title_canon_sha256":"18df28346fd74adb37e340c53d3269a236a3389eb0b355be2b77ae8bd5ef87e2"},"schema_version":"1.0","source":{"id":"1511.03723","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03723","created_at":"2026-05-18T00:45:08Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03723v1","created_at":"2026-05-18T00:45:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03723","created_at":"2026-05-18T00:45:08Z"},{"alias_kind":"pith_short_12","alias_value":"CPEE2JNMLQZI","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CPEE2JNMLQZIMIPL","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CPEE2JNM","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:5e2757dcc07b7c6ebc006a8d968d76b3c25f1ec0b1ec571497074c361e40bd5c","target":"graph","created_at":"2026-05-18T00:45:08Z","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":"This paper considers the propagation of TE-modes in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a periodic background medium. Both the periodic background problem and the perturbed problem are modelled by a divergence type equation. A feature of our analysis is that we allow discontinuities in the coefficients of the operator, which is required to model many photonic crystals. It is shown that arbitrarily weak perturbations introduce spectrum into the spectral gaps of the background operator.","authors_text":"Ian Wood, Malcolm Brown, Maria Radosz, Michael Plum, Vu Hoang","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-11T23:08:31Z","title":"Gap localization of TE-Modes by arbitrarily weak defects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03723","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:c4ad3c5ccf9ef5ab4d1a0a44e0c3e9263dc75e076321be0fa5175f1b85e59ad5","target":"record","created_at":"2026-05-18T00:45:08Z","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":"d0321cb85d9f757faed5ff0493d5254c6e11ccc17535d72628e47942e46c0448","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-11T23:08:31Z","title_canon_sha256":"18df28346fd74adb37e340c53d3269a236a3389eb0b355be2b77ae8bd5ef87e2"},"schema_version":"1.0","source":{"id":"1511.03723","kind":"arxiv","version":1}},"canonical_sha256":"13c84d25ac5c328621eb3d603530cd6fd593734da4e417039177f1933a144bd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13c84d25ac5c328621eb3d603530cd6fd593734da4e417039177f1933a144bd2","first_computed_at":"2026-05-18T00:45:08.538968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:08.538968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lwvHfBCeBH93xUFJdMTnkLeAxpo7gmWzvyzptpy0krBQoHhbYMJ9GamEU/tSoCGslC/uvD4sI0rfzU8aDBRxDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:08.539667Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.03723","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4ad3c5ccf9ef5ab4d1a0a44e0c3e9263dc75e076321be0fa5175f1b85e59ad5","sha256:5e2757dcc07b7c6ebc006a8d968d76b3c25f1ec0b1ec571497074c361e40bd5c"],"state_sha256":"18c9ab95e9a5ed23745b3cd36bf1d2d4c193daa1e4656371f40bc694deac8798"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dE3dhtMu3vZNlkQZQNLfENTn7a3E4s15LV6OWk9bj2Zsqr3ils5i83+aYOKSOzTar6GQigjNeT6idvgrrNJPBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T19:46:44.808873Z","bundle_sha256":"0e27f7791839613467998fceb3b2455b43136c155cf6ce7ef542ce7c57e2f364"}}