{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3UN2FDO7ZAV3BAF3RHVQI3Q3JI","short_pith_number":"pith:3UN2FDO7","canonical_record":{"source":{"id":"1309.0080","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"physics.optics","submitted_at":"2013-08-31T09:07:18Z","cross_cats_sorted":[],"title_canon_sha256":"3fe833667a846066d7f517c1220722dedad991a8d77cc3c25bd271b17d7c0c72","abstract_canon_sha256":"282f55391176e7e9254a7e488d8f4bb01e391c6cfab510e7a0624e3c5c521a90"},"schema_version":"1.0"},"canonical_sha256":"dd1ba28ddfc82bb080bb89eb046e1b4a1661cae30e383ee0e65bc82aa2567a38","source":{"kind":"arxiv","id":"1309.0080","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0080","created_at":"2026-05-18T03:03:56Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0080v2","created_at":"2026-05-18T03:03:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0080","created_at":"2026-05-18T03:03:56Z"},{"alias_kind":"pith_short_12","alias_value":"3UN2FDO7ZAV3","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3UN2FDO7ZAV3BAF3","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3UN2FDO7","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3UN2FDO7ZAV3BAF3RHVQI3Q3JI","target":"record","payload":{"canonical_record":{"source":{"id":"1309.0080","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"physics.optics","submitted_at":"2013-08-31T09:07:18Z","cross_cats_sorted":[],"title_canon_sha256":"3fe833667a846066d7f517c1220722dedad991a8d77cc3c25bd271b17d7c0c72","abstract_canon_sha256":"282f55391176e7e9254a7e488d8f4bb01e391c6cfab510e7a0624e3c5c521a90"},"schema_version":"1.0"},"canonical_sha256":"dd1ba28ddfc82bb080bb89eb046e1b4a1661cae30e383ee0e65bc82aa2567a38","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:56.532094Z","signature_b64":"M4vLV9QyAnNJiAYip47/iyFa4RU+2LcchxwzEWyxu1Bork4y3eI9plip83zxrOHpQwwPQXpRhccU2uCzMojcDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd1ba28ddfc82bb080bb89eb046e1b4a1661cae30e383ee0e65bc82aa2567a38","last_reissued_at":"2026-05-18T03:03:56.531356Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:56.531356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.0080","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:03:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1I/BnZz1KLAYdVl4TbRWAhUlRCU5q4GiIFB2BBSyEsmCApEhTU2bNwqwKMBFG98rEoXTGED4tCi7/2jUHAAeBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:17:00.269643Z"},"content_sha256":"48e7f25f2753256299d8c1f15ca749e94270df3bad9453780694c4fe89e34be2","schema_version":"1.0","event_id":"sha256:48e7f25f2753256299d8c1f15ca749e94270df3bad9453780694c4fe89e34be2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3UN2FDO7ZAV3BAF3RHVQI3Q3JI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effect of loss on the dispersion relation of photonic and phononic crystals","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"physics.optics","authors_text":"Alejandro Martinez, Jose Maria Escalante, Vincent Laude","submitted_at":"2013-08-31T09:07:18Z","abstract_excerpt":"A theoretical analysis is made of the transformation of the dispersion relation of waves in artificial crystals under the influence of loss, including the case of photonic and phononic crystals. Considering a general dispersion relation in implicit form, an analytic procedure is derived to obtain the transformed dispersion relation. It is shown that the dispersion relation is generally shifted in the complex $(k,\\omega)$ plane, with $k$ the wavenumber and $\\omega$ the angular frequency. The value of the shift is obtained explicitly as a function of the perturbation of material constants accoun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0080","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:03:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fLoA/8OrmrC7/uVL9nluaqAcozwnOlvAHh6EVH5KgvsRf8Sw/ND5OZp1y5veY1bp+Pj2gmjScmwCU0Lb0yIBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:17:00.269988Z"},"content_sha256":"727c9e982c8b71ed329a38c4492adbed3950ce0d0a0d6871052a0cb6b5895b36","schema_version":"1.0","event_id":"sha256:727c9e982c8b71ed329a38c4492adbed3950ce0d0a0d6871052a0cb6b5895b36"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3UN2FDO7ZAV3BAF3RHVQI3Q3JI/bundle.json","state_url":"https://pith.science/pith/3UN2FDO7ZAV3BAF3RHVQI3Q3JI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3UN2FDO7ZAV3BAF3RHVQI3Q3JI/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":"2026-06-03T21:17:00Z","links":{"resolver":"https://pith.science/pith/3UN2FDO7ZAV3BAF3RHVQI3Q3JI","bundle":"https://pith.science/pith/3UN2FDO7ZAV3BAF3RHVQI3Q3JI/bundle.json","state":"https://pith.science/pith/3UN2FDO7ZAV3BAF3RHVQI3Q3JI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3UN2FDO7ZAV3BAF3RHVQI3Q3JI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3UN2FDO7ZAV3BAF3RHVQI3Q3JI","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":"282f55391176e7e9254a7e488d8f4bb01e391c6cfab510e7a0624e3c5c521a90","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"physics.optics","submitted_at":"2013-08-31T09:07:18Z","title_canon_sha256":"3fe833667a846066d7f517c1220722dedad991a8d77cc3c25bd271b17d7c0c72"},"schema_version":"1.0","source":{"id":"1309.0080","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0080","created_at":"2026-05-18T03:03:56Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0080v2","created_at":"2026-05-18T03:03:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0080","created_at":"2026-05-18T03:03:56Z"},{"alias_kind":"pith_short_12","alias_value":"3UN2FDO7ZAV3","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3UN2FDO7ZAV3BAF3","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3UN2FDO7","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:727c9e982c8b71ed329a38c4492adbed3950ce0d0a0d6871052a0cb6b5895b36","target":"graph","created_at":"2026-05-18T03:03:56Z","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":"A theoretical analysis is made of the transformation of the dispersion relation of waves in artificial crystals under the influence of loss, including the case of photonic and phononic crystals. Considering a general dispersion relation in implicit form, an analytic procedure is derived to obtain the transformed dispersion relation. It is shown that the dispersion relation is generally shifted in the complex $(k,\\omega)$ plane, with $k$ the wavenumber and $\\omega$ the angular frequency. The value of the shift is obtained explicitly as a function of the perturbation of material constants accoun","authors_text":"Alejandro Martinez, Jose Maria Escalante, Vincent Laude","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"physics.optics","submitted_at":"2013-08-31T09:07:18Z","title":"Effect of loss on the dispersion relation of photonic and phononic crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0080","kind":"arxiv","version":2},"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":"sha256:48e7f25f2753256299d8c1f15ca749e94270df3bad9453780694c4fe89e34be2","target":"record","created_at":"2026-05-18T03:03:56Z","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":"282f55391176e7e9254a7e488d8f4bb01e391c6cfab510e7a0624e3c5c521a90","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"physics.optics","submitted_at":"2013-08-31T09:07:18Z","title_canon_sha256":"3fe833667a846066d7f517c1220722dedad991a8d77cc3c25bd271b17d7c0c72"},"schema_version":"1.0","source":{"id":"1309.0080","kind":"arxiv","version":2}},"canonical_sha256":"dd1ba28ddfc82bb080bb89eb046e1b4a1661cae30e383ee0e65bc82aa2567a38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd1ba28ddfc82bb080bb89eb046e1b4a1661cae30e383ee0e65bc82aa2567a38","first_computed_at":"2026-05-18T03:03:56.531356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:56.531356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M4vLV9QyAnNJiAYip47/iyFa4RU+2LcchxwzEWyxu1Bork4y3eI9plip83zxrOHpQwwPQXpRhccU2uCzMojcDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:56.532094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0080","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48e7f25f2753256299d8c1f15ca749e94270df3bad9453780694c4fe89e34be2","sha256:727c9e982c8b71ed329a38c4492adbed3950ce0d0a0d6871052a0cb6b5895b36"],"state_sha256":"2d36b069d65b6f02120513a4df766ab73504697453dd15658ba7aaddebae0f08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JOmKBxAKh1bGGjcq897VYc2ByIKiVyNcP64uZsZwTSBvU5jcLQa+PGMhY1u7m+o2D7Qb0S7uwC/FiQSXVLnOCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T21:17:00.271972Z","bundle_sha256":"d10a7f45a1ba27605099891ee3dce71cb3bd15300c2422e165f6e58b09b0b58d"}}