{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ECNDOO3W2FO22PF2SRLWI7THQM","short_pith_number":"pith:ECNDOO3W","canonical_record":{"source":{"id":"1411.6420","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2014-11-24T11:53:26Z","cross_cats_sorted":[],"title_canon_sha256":"39212a6de9ee205be1d891711bacb40ce3f672b2fd498bb7141bdf7decbb64f0","abstract_canon_sha256":"cc1c0eb0d81ec67428e78404682558331bb14d22d7ad9f5aedc567e703699e71"},"schema_version":"1.0"},"canonical_sha256":"209a373b76d15dad3cba9457647e67832dce072fa8846236ce01d3fcfcbbd6b1","source":{"kind":"arxiv","id":"1411.6420","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6420","created_at":"2026-05-18T02:19:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6420v3","created_at":"2026-05-18T02:19:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6420","created_at":"2026-05-18T02:19:52Z"},{"alias_kind":"pith_short_12","alias_value":"ECNDOO3W2FO2","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"ECNDOO3W2FO22PF2","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"ECNDOO3W","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ECNDOO3W2FO22PF2SRLWI7THQM","target":"record","payload":{"canonical_record":{"source":{"id":"1411.6420","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2014-11-24T11:53:26Z","cross_cats_sorted":[],"title_canon_sha256":"39212a6de9ee205be1d891711bacb40ce3f672b2fd498bb7141bdf7decbb64f0","abstract_canon_sha256":"cc1c0eb0d81ec67428e78404682558331bb14d22d7ad9f5aedc567e703699e71"},"schema_version":"1.0"},"canonical_sha256":"209a373b76d15dad3cba9457647e67832dce072fa8846236ce01d3fcfcbbd6b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:52.741171Z","signature_b64":"A6fnviqYInSiHTcnVC8jeYSM93rxOs4TMQgwVtMEP6cpNAED9blWT9hto/WdoshmZJWDLuZYE6EtaDPFues3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"209a373b76d15dad3cba9457647e67832dce072fa8846236ce01d3fcfcbbd6b1","last_reissued_at":"2026-05-18T02:19:52.740497Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:52.740497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.6420","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:19:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nDHfuyF/FTBf4ZXeF7B5WLKMz2uWS7cZSXVG+iyvspqyM6GRfwc8n0IUV7ApIafYuMmDveRcDqJgnqMQ1vK/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:23:49.528183Z"},"content_sha256":"988b6da20f44537ef7b674e3b0e74a13ab2626c886d2bcc08a8f8a3752462559","schema_version":"1.0","event_id":"sha256:988b6da20f44537ef7b674e3b0e74a13ab2626c886d2bcc08a8f8a3752462559"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ECNDOO3W2FO22PF2SRLWI7THQM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Hilbert transform: Applications to atomic spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.atom-ph","authors_text":"C. S. Adams, I. G. Hughes, J. Keaveney, K. A. Whittaker","submitted_at":"2014-11-24T11:53:26Z","abstract_excerpt":"In many areas of physics, the Kramers-Kronig (KK) relations are used to extract information about the real part of the optical response of a medium from its imaginary counterpart. In this paper we discuss an alternative but mathematically equivalent approach based on the Hilbert transform. We apply the Hilbert transform to transmission spectra to find the group and refractive indices of a Cs vapor, and thereby demonstrate how the Hilbert transform allows indirect measurement of the refractive index, group index and group delay whilst avoiding the use of complicated experimental set ups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6420","kind":"arxiv","version":3},"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":"2026-05-18T02:19:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nqI2E/BwUqLz80RFwha76fqdAzWRTCULvsZfzTd7khu1I3TpWY3V4MTvaeeDwpzIWVlfEgwroowFQIeL1av3DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:23:49.529309Z"},"content_sha256":"7070c9d30331bd6318bcf433dad00aae9faad64208cec2a0db17e78fdd7a07b6","schema_version":"1.0","event_id":"sha256:7070c9d30331bd6318bcf433dad00aae9faad64208cec2a0db17e78fdd7a07b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ECNDOO3W2FO22PF2SRLWI7THQM/bundle.json","state_url":"https://pith.science/pith/ECNDOO3W2FO22PF2SRLWI7THQM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ECNDOO3W2FO22PF2SRLWI7THQM/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":"2026-05-31T22:23:49Z","links":{"resolver":"https://pith.science/pith/ECNDOO3W2FO22PF2SRLWI7THQM","bundle":"https://pith.science/pith/ECNDOO3W2FO22PF2SRLWI7THQM/bundle.json","state":"https://pith.science/pith/ECNDOO3W2FO22PF2SRLWI7THQM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ECNDOO3W2FO22PF2SRLWI7THQM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ECNDOO3W2FO22PF2SRLWI7THQM","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":"cc1c0eb0d81ec67428e78404682558331bb14d22d7ad9f5aedc567e703699e71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2014-11-24T11:53:26Z","title_canon_sha256":"39212a6de9ee205be1d891711bacb40ce3f672b2fd498bb7141bdf7decbb64f0"},"schema_version":"1.0","source":{"id":"1411.6420","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6420","created_at":"2026-05-18T02:19:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6420v3","created_at":"2026-05-18T02:19:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6420","created_at":"2026-05-18T02:19:52Z"},{"alias_kind":"pith_short_12","alias_value":"ECNDOO3W2FO2","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"ECNDOO3W2FO22PF2","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"ECNDOO3W","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:7070c9d30331bd6318bcf433dad00aae9faad64208cec2a0db17e78fdd7a07b6","target":"graph","created_at":"2026-05-18T02:19:52Z","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":"In many areas of physics, the Kramers-Kronig (KK) relations are used to extract information about the real part of the optical response of a medium from its imaginary counterpart. In this paper we discuss an alternative but mathematically equivalent approach based on the Hilbert transform. We apply the Hilbert transform to transmission spectra to find the group and refractive indices of a Cs vapor, and thereby demonstrate how the Hilbert transform allows indirect measurement of the refractive index, group index and group delay whilst avoiding the use of complicated experimental set ups.","authors_text":"C. S. Adams, I. G. Hughes, J. Keaveney, K. A. Whittaker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2014-11-24T11:53:26Z","title":"The Hilbert transform: Applications to atomic spectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6420","kind":"arxiv","version":3},"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":"sha256:988b6da20f44537ef7b674e3b0e74a13ab2626c886d2bcc08a8f8a3752462559","target":"record","created_at":"2026-05-18T02:19:52Z","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":"cc1c0eb0d81ec67428e78404682558331bb14d22d7ad9f5aedc567e703699e71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2014-11-24T11:53:26Z","title_canon_sha256":"39212a6de9ee205be1d891711bacb40ce3f672b2fd498bb7141bdf7decbb64f0"},"schema_version":"1.0","source":{"id":"1411.6420","kind":"arxiv","version":3}},"canonical_sha256":"209a373b76d15dad3cba9457647e67832dce072fa8846236ce01d3fcfcbbd6b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"209a373b76d15dad3cba9457647e67832dce072fa8846236ce01d3fcfcbbd6b1","first_computed_at":"2026-05-18T02:19:52.740497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:52.740497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A6fnviqYInSiHTcnVC8jeYSM93rxOs4TMQgwVtMEP6cpNAED9blWT9hto/WdoshmZJWDLuZYE6EtaDPFues3CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:52.741171Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.6420","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:988b6da20f44537ef7b674e3b0e74a13ab2626c886d2bcc08a8f8a3752462559","sha256:7070c9d30331bd6318bcf433dad00aae9faad64208cec2a0db17e78fdd7a07b6"],"state_sha256":"343c7cb792dcc8d49c72b74d9b25eb1255fff5244e9efd0865389d0bc4a0c9f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2EJnlZjuneFQNhRqzIvgAJS9ZQBcQYHuvtR17T2dDVFS4DDr+6wUWgLWNvbzFK4O2fuIjmNkxjTpV3Tw8c6BDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T22:23:49.532846Z","bundle_sha256":"602e5b93ca5e797fe476348edd45fcab277fd2990ea94ccf4fecf1d32faf6e9d"}}