{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:XWGFJIBIMVDJ4KKTIGXGH3FRZH","short_pith_number":"pith:XWGFJIBI","canonical_record":{"source":{"id":"0709.0142","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2007-09-03T01:56:05Z","cross_cats_sorted":[],"title_canon_sha256":"651872e640c55157c16567e01cd60331c4ed89cd7657a94dacff4aaf27ddc717","abstract_canon_sha256":"b44acc8e3db648f35bc2e5db66573da1e0fffea4d3425b6be7f081cd2a99f007"},"schema_version":"1.0"},"canonical_sha256":"bd8c54a02865469e295341ae63ecb1c9c5642ca858bbb6fb6cc1b8af849fd19c","source":{"kind":"arxiv","id":"0709.0142","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.0142","created_at":"2026-07-04T15:10:10Z"},{"alias_kind":"arxiv_version","alias_value":"0709.0142v2","created_at":"2026-07-04T15:10:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.0142","created_at":"2026-07-04T15:10:10Z"},{"alias_kind":"pith_short_12","alias_value":"XWGFJIBIMVDJ","created_at":"2026-07-04T15:10:10Z"},{"alias_kind":"pith_short_16","alias_value":"XWGFJIBIMVDJ4KKT","created_at":"2026-07-04T15:10:10Z"},{"alias_kind":"pith_short_8","alias_value":"XWGFJIBI","created_at":"2026-07-04T15:10:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:XWGFJIBIMVDJ4KKTIGXGH3FRZH","target":"record","payload":{"canonical_record":{"source":{"id":"0709.0142","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2007-09-03T01:56:05Z","cross_cats_sorted":[],"title_canon_sha256":"651872e640c55157c16567e01cd60331c4ed89cd7657a94dacff4aaf27ddc717","abstract_canon_sha256":"b44acc8e3db648f35bc2e5db66573da1e0fffea4d3425b6be7f081cd2a99f007"},"schema_version":"1.0"},"canonical_sha256":"bd8c54a02865469e295341ae63ecb1c9c5642ca858bbb6fb6cc1b8af849fd19c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:10:10.633137Z","signature_b64":"NbCPDLt+s8YawZjV3HnYvuTM4vM54ItEg5PIQTlCqYrnvpS0aUllbTL+JB9mKLL5FVEKu3sMPuT0uoFEFuqvBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd8c54a02865469e295341ae63ecb1c9c5642ca858bbb6fb6cc1b8af849fd19c","last_reissued_at":"2026-07-04T15:10:10.632717Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:10:10.632717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0709.0142","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":"2026-07-04T15:10:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1bVFs3vJQrVU44WMijmY7BQJ9bOVHesa/E+wPhz2RXC80CzGxHgIbOMhuoP8mFGo/bTc8ugYDNyGtlkoPi7ZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:07:29.488988Z"},"content_sha256":"5dcee2bab8c708df5df174393fb3cb5610759d1f126c77b385726a8b45844fca","schema_version":"1.0","event_id":"sha256:5dcee2bab8c708df5df174393fb3cb5610759d1f126c77b385726a8b45844fca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:XWGFJIBIMVDJ4KKTIGXGH3FRZH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Reference Frames and the Classification of Rotationally-Invariant Maps","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"J.-C. Boileau, L. Sheridan, M. Laforest, S. D. Bartlett","submitted_at":"2007-09-03T01:56:05Z","abstract_excerpt":"We give a convenient representation for any map that is covariant with respect to an irreducible representation of SU(2), and use this representation to analyze the evolution of a quantum directional reference frame when it is exploited as a resource for performing quantum operations. We introduce the moments of a quantum reference frame, which serve as a complete description of its properties as a frame, and investigate how many times a quantum directional reference frame represented by a spin-j system can be used to perform a certain quantum operation with a given probability of success. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.0142","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0709.0142/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:10:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c/MjZVb2dSOzK82RpUtUYE8Y2Sw8SePsw6iD6HsL1N1laXbiQNqLrxmrdit/bqrwES/bUlR67D9jLhIskSblAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:07:29.489722Z"},"content_sha256":"83f772266feb07219be5dbc0a8b6f945cdb26db1076cb07cbc006c39cbc5c8c8","schema_version":"1.0","event_id":"sha256:83f772266feb07219be5dbc0a8b6f945cdb26db1076cb07cbc006c39cbc5c8c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XWGFJIBIMVDJ4KKTIGXGH3FRZH/bundle.json","state_url":"https://pith.science/pith/XWGFJIBIMVDJ4KKTIGXGH3FRZH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XWGFJIBIMVDJ4KKTIGXGH3FRZH/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":"2026-08-13T17:07:29Z","links":{"resolver":"https://pith.science/pith/XWGFJIBIMVDJ4KKTIGXGH3FRZH","bundle":"https://pith.science/pith/XWGFJIBIMVDJ4KKTIGXGH3FRZH/bundle.json","state":"https://pith.science/pith/XWGFJIBIMVDJ4KKTIGXGH3FRZH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XWGFJIBIMVDJ4KKTIGXGH3FRZH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:XWGFJIBIMVDJ4KKTIGXGH3FRZH","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":"b44acc8e3db648f35bc2e5db66573da1e0fffea4d3425b6be7f081cd2a99f007","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2007-09-03T01:56:05Z","title_canon_sha256":"651872e640c55157c16567e01cd60331c4ed89cd7657a94dacff4aaf27ddc717"},"schema_version":"1.0","source":{"id":"0709.0142","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.0142","created_at":"2026-07-04T15:10:10Z"},{"alias_kind":"arxiv_version","alias_value":"0709.0142v2","created_at":"2026-07-04T15:10:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.0142","created_at":"2026-07-04T15:10:10Z"},{"alias_kind":"pith_short_12","alias_value":"XWGFJIBIMVDJ","created_at":"2026-07-04T15:10:10Z"},{"alias_kind":"pith_short_16","alias_value":"XWGFJIBIMVDJ4KKT","created_at":"2026-07-04T15:10:10Z"},{"alias_kind":"pith_short_8","alias_value":"XWGFJIBI","created_at":"2026-07-04T15:10:10Z"}],"graph_snapshots":[{"event_id":"sha256:83f772266feb07219be5dbc0a8b6f945cdb26db1076cb07cbc006c39cbc5c8c8","target":"graph","created_at":"2026-07-04T15:10:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0709.0142/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a convenient representation for any map that is covariant with respect to an irreducible representation of SU(2), and use this representation to analyze the evolution of a quantum directional reference frame when it is exploited as a resource for performing quantum operations. We introduce the moments of a quantum reference frame, which serve as a complete description of its properties as a frame, and investigate how many times a quantum directional reference frame represented by a spin-j system can be used to perform a certain quantum operation with a given probability of success. We ","authors_text":"J.-C. Boileau, L. Sheridan, M. Laforest, S. D. Bartlett","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2007-09-03T01:56:05Z","title":"Quantum Reference Frames and the Classification of Rotationally-Invariant Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.0142","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":"sha256:5dcee2bab8c708df5df174393fb3cb5610759d1f126c77b385726a8b45844fca","target":"record","created_at":"2026-07-04T15:10:10Z","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":"b44acc8e3db648f35bc2e5db66573da1e0fffea4d3425b6be7f081cd2a99f007","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2007-09-03T01:56:05Z","title_canon_sha256":"651872e640c55157c16567e01cd60331c4ed89cd7657a94dacff4aaf27ddc717"},"schema_version":"1.0","source":{"id":"0709.0142","kind":"arxiv","version":2}},"canonical_sha256":"bd8c54a02865469e295341ae63ecb1c9c5642ca858bbb6fb6cc1b8af849fd19c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd8c54a02865469e295341ae63ecb1c9c5642ca858bbb6fb6cc1b8af849fd19c","first_computed_at":"2026-07-04T15:10:10.632717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:10:10.632717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NbCPDLt+s8YawZjV3HnYvuTM4vM54ItEg5PIQTlCqYrnvpS0aUllbTL+JB9mKLL5FVEKu3sMPuT0uoFEFuqvBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:10:10.633137Z","signed_message":"canonical_sha256_bytes"},"source_id":"0709.0142","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dcee2bab8c708df5df174393fb3cb5610759d1f126c77b385726a8b45844fca","sha256:83f772266feb07219be5dbc0a8b6f945cdb26db1076cb07cbc006c39cbc5c8c8"],"state_sha256":"a062a4a1d1bef018b7abe06a97ad7f72c92d62b88a746fb6321e55550cf44ce9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vXzInEv4o7HZRAQMLpUeF2hMAlKx6g2+MONaWk2nmiud4D36CwHziXUkEgXaWU1bCWygby8cZYNXVgOCiKATCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T17:07:29.521582Z","bundle_sha256":"23ab0b3c6857d1ff7f0fdbfa74dee5075f51772a8222cc6f3b76c01a3e97da68"}}