{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:PBKE265QWEQGW47R755SW6LUVT","short_pith_number":"pith:PBKE265Q","canonical_record":{"source":{"id":"quant-ph/0209101","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2002-09-17T10:46:24Z","cross_cats_sorted":[],"title_canon_sha256":"187cef80c94b68f20468ddc72b4ecf29b1d717154b5c3bb1b12b43c4df52b92a","abstract_canon_sha256":"5290190a1570ee3de155d89c877f13fb67b0eb9a6c582ce59eb9c59517417456"},"schema_version":"1.0"},"canonical_sha256":"78544d7bb0b1206b73f1ff7b2b7974acce7f06b5e6dabbaed07e33d6788bc17e","source":{"kind":"arxiv","id":"quant-ph/0209101","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0209101","created_at":"2026-05-18T01:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0209101v1","created_at":"2026-05-18T01:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0209101","created_at":"2026-05-18T01:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"PBKE265QWEQG","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"PBKE265QWEQGW47R","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"PBKE265Q","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:PBKE265QWEQGW47R755SW6LUVT","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0209101","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2002-09-17T10:46:24Z","cross_cats_sorted":[],"title_canon_sha256":"187cef80c94b68f20468ddc72b4ecf29b1d717154b5c3bb1b12b43c4df52b92a","abstract_canon_sha256":"5290190a1570ee3de155d89c877f13fb67b0eb9a6c582ce59eb9c59517417456"},"schema_version":"1.0"},"canonical_sha256":"78544d7bb0b1206b73f1ff7b2b7974acce7f06b5e6dabbaed07e33d6788bc17e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:59.857891Z","signature_b64":"2gjnsIS/DP6JsK8W96319FxjgwCc5V6b/N2Ak5qkmnlBbzaP6SKNBu9BhWHg1tTvjTiZiHNjEnR6cXE4r2xOCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78544d7bb0b1206b73f1ff7b2b7974acce7f06b5e6dabbaed07e33d6788bc17e","last_reissued_at":"2026-05-18T01:37:59.857198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:59.857198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0209101","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":"2026-05-18T01:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S+7wTN4S2XqK1xpxwRg8l0I84cVJ0Oqulqz2Dk2X2RxiYoT37ObACjIFGD8QAVnCjdY7fTYvJe6z42qHLkjjCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:07:14.743951Z"},"content_sha256":"73ab8de7aebbd2b25aa3e0ba190502a5be8f135d35e722d5c776afe743c6d55b","schema_version":"1.0","event_id":"sha256:73ab8de7aebbd2b25aa3e0ba190502a5be8f135d35e722d5c776afe743c6d55b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:PBKE265QWEQGW47R755SW6LUVT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Covariant phase difference observables","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"J.-P. Pellonpaa, P. Lahti, T. Heinonen","submitted_at":"2002-09-17T10:46:24Z","abstract_excerpt":"Covariant phase difference observables are determined in two different ways, by a direct computation and by a group theoretical method. A characterization of phase difference observables which can be expressed as difference of two phase observables is given. Classical limit of such phase difference observables are determined and the Pegg-Barnett phase difference distribution is obtained from the phase difference representation. The relation of Ban's theory to the covariant phase theories is exhibited."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0209101","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":"2026-05-18T01:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WKf/LVLgLcKcC+jz/0oRPbqFmzBieEy1NHKqcmUD8i4V/GC8O+RuMoyoSECVBaTvC4tq1EbOq2NYpo2LxlDCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:07:14.744761Z"},"content_sha256":"1d444d7901b31b70577f3bce94b96a9663c3653beee07b8a924bb205044d929d","schema_version":"1.0","event_id":"sha256:1d444d7901b31b70577f3bce94b96a9663c3653beee07b8a924bb205044d929d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PBKE265QWEQGW47R755SW6LUVT/bundle.json","state_url":"https://pith.science/pith/PBKE265QWEQGW47R755SW6LUVT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PBKE265QWEQGW47R755SW6LUVT/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":"2026-05-31T11:07:14Z","links":{"resolver":"https://pith.science/pith/PBKE265QWEQGW47R755SW6LUVT","bundle":"https://pith.science/pith/PBKE265QWEQGW47R755SW6LUVT/bundle.json","state":"https://pith.science/pith/PBKE265QWEQGW47R755SW6LUVT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PBKE265QWEQGW47R755SW6LUVT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:PBKE265QWEQGW47R755SW6LUVT","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":"5290190a1570ee3de155d89c877f13fb67b0eb9a6c582ce59eb9c59517417456","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2002-09-17T10:46:24Z","title_canon_sha256":"187cef80c94b68f20468ddc72b4ecf29b1d717154b5c3bb1b12b43c4df52b92a"},"schema_version":"1.0","source":{"id":"quant-ph/0209101","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0209101","created_at":"2026-05-18T01:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0209101v1","created_at":"2026-05-18T01:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0209101","created_at":"2026-05-18T01:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"PBKE265QWEQG","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"PBKE265QWEQGW47R","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"PBKE265Q","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:1d444d7901b31b70577f3bce94b96a9663c3653beee07b8a924bb205044d929d","target":"graph","created_at":"2026-05-18T01:37:59Z","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":"Covariant phase difference observables are determined in two different ways, by a direct computation and by a group theoretical method. A characterization of phase difference observables which can be expressed as difference of two phase observables is given. Classical limit of such phase difference observables are determined and the Pegg-Barnett phase difference distribution is obtained from the phase difference representation. The relation of Ban's theory to the covariant phase theories is exhibited.","authors_text":"J.-P. Pellonpaa, P. Lahti, T. Heinonen","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2002-09-17T10:46:24Z","title":"Covariant phase difference observables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0209101","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":"sha256:73ab8de7aebbd2b25aa3e0ba190502a5be8f135d35e722d5c776afe743c6d55b","target":"record","created_at":"2026-05-18T01:37:59Z","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":"5290190a1570ee3de155d89c877f13fb67b0eb9a6c582ce59eb9c59517417456","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2002-09-17T10:46:24Z","title_canon_sha256":"187cef80c94b68f20468ddc72b4ecf29b1d717154b5c3bb1b12b43c4df52b92a"},"schema_version":"1.0","source":{"id":"quant-ph/0209101","kind":"arxiv","version":1}},"canonical_sha256":"78544d7bb0b1206b73f1ff7b2b7974acce7f06b5e6dabbaed07e33d6788bc17e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78544d7bb0b1206b73f1ff7b2b7974acce7f06b5e6dabbaed07e33d6788bc17e","first_computed_at":"2026-05-18T01:37:59.857198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:59.857198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2gjnsIS/DP6JsK8W96319FxjgwCc5V6b/N2Ak5qkmnlBbzaP6SKNBu9BhWHg1tTvjTiZiHNjEnR6cXE4r2xOCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:59.857891Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0209101","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73ab8de7aebbd2b25aa3e0ba190502a5be8f135d35e722d5c776afe743c6d55b","sha256:1d444d7901b31b70577f3bce94b96a9663c3653beee07b8a924bb205044d929d"],"state_sha256":"59deae25ca79b8955fafd5408817968907f94a717036caeef0537ad100f1b572"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qs9LAPwbdbWSwBWZuRHqWpPmARkqCAY4RsQSG+PjUUjoqu7Jtp0GxzICmE7Q9nj6pcxgoU05riohyUUZyv94AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:07:14.749052Z","bundle_sha256":"1ec0d7f6e0c77e64033ba1c32514d7a2d4088e4ee5791a7dc9f2ca7b15b2c590"}}