{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:WFFSQUAU572YW6WEZX532LVXIO","short_pith_number":"pith:WFFSQUAU","canonical_record":{"source":{"id":"quant-ph/0407257","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2004-07-30T06:02:39Z","cross_cats_sorted":[],"title_canon_sha256":"6142c03f1841e11fa0cb3b76154e95be15b7abe1dc0c5775451cf2bca4f870fe","abstract_canon_sha256":"289efcccaf66dd97cb1b73daa1692fadfd7e9db671f3585bd590b27a97fb5a5a"},"schema_version":"1.0"},"canonical_sha256":"b14b285014eff58b7ac4cdfbbd2eb743b8586badeae4df29aaf2262e34806be7","source":{"kind":"arxiv","id":"quant-ph/0407257","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0407257","created_at":"2026-07-04T16:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0407257v2","created_at":"2026-07-04T16:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0407257","created_at":"2026-07-04T16:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"WFFSQUAU572Y","created_at":"2026-07-04T16:50:22Z"},{"alias_kind":"pith_short_16","alias_value":"WFFSQUAU572YW6WE","created_at":"2026-07-04T16:50:22Z"},{"alias_kind":"pith_short_8","alias_value":"WFFSQUAU","created_at":"2026-07-04T16:50:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:WFFSQUAU572YW6WEZX532LVXIO","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0407257","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2004-07-30T06:02:39Z","cross_cats_sorted":[],"title_canon_sha256":"6142c03f1841e11fa0cb3b76154e95be15b7abe1dc0c5775451cf2bca4f870fe","abstract_canon_sha256":"289efcccaf66dd97cb1b73daa1692fadfd7e9db671f3585bd590b27a97fb5a5a"},"schema_version":"1.0"},"canonical_sha256":"b14b285014eff58b7ac4cdfbbd2eb743b8586badeae4df29aaf2262e34806be7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:50:22.313251Z","signature_b64":"wkSXtChJTDmIbJegWE2Uwq+m/Uqfm2quIS4x6GRFsj2GfFfsTYFJAo/A9bDCKozTATX8gvfNj59JZKbfaLMJDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b14b285014eff58b7ac4cdfbbd2eb743b8586badeae4df29aaf2262e34806be7","last_reissued_at":"2026-07-04T16:50:22.312894Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:50:22.312894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0407257","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":"2026-07-04T16:50:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iiik4EQjiDCDsTmLkOto/gKvpggtYcVKfEVzph0o/LNxT3v3vDwWgtt+9sRcmsLovIT1Lu8+tEnO68yqjhMUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T14:40:58.265968Z"},"content_sha256":"191477e1fc07b91284b3d006507d79b91c32700b635a1b98dc3be507cdc941ae","schema_version":"1.0","event_id":"sha256:191477e1fc07b91284b3d006507d79b91c32700b635a1b98dc3be507cdc941ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:WFFSQUAU572YW6WEZX532LVXIO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wigner-Weyl isomorphism for quantum mechanics on Lie groups","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alessandro Zampini, G. Marmo, N. Mukunda, R.Simon, S. Chaturvedi","submitted_at":"2004-07-30T06:02:39Z","abstract_excerpt":"The Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group $G$ is developed in detail. Several New features are shown to arise which have no counterparts in the familiar Cartesian case. Notable among these is the notion of a `semiquantised phase space', a structure on which the Weyl symbols of operators turn out to be naturally defined and, figuratively speaking, located midway between the classical phase space $T^*G$ and the Hilbert space of square integrable functions on $G$. General expressions for the star product for Weyl symbols are presented and explicitly worked ou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0407257","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/quant-ph/0407257/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":"2026-07-04T16:50:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OfB1rDz/Nqe6sJrNYYwbFkjr9NdtQwDvPMw6LbxCchZ5J9x05DO2gRAYXMDeCzvlBCPTu8HitZn5YeqqYyUUAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T14:40:58.266449Z"},"content_sha256":"1eef0339e01155eb54677b61e761211cb35d6925054de1e78ba2c87eb482db8e","schema_version":"1.0","event_id":"sha256:1eef0339e01155eb54677b61e761211cb35d6925054de1e78ba2c87eb482db8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WFFSQUAU572YW6WEZX532LVXIO/bundle.json","state_url":"https://pith.science/pith/WFFSQUAU572YW6WEZX532LVXIO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WFFSQUAU572YW6WEZX532LVXIO/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":"2026-08-10T14:40:58Z","links":{"resolver":"https://pith.science/pith/WFFSQUAU572YW6WEZX532LVXIO","bundle":"https://pith.science/pith/WFFSQUAU572YW6WEZX532LVXIO/bundle.json","state":"https://pith.science/pith/WFFSQUAU572YW6WEZX532LVXIO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WFFSQUAU572YW6WEZX532LVXIO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:WFFSQUAU572YW6WEZX532LVXIO","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":"289efcccaf66dd97cb1b73daa1692fadfd7e9db671f3585bd590b27a97fb5a5a","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-07-30T06:02:39Z","title_canon_sha256":"6142c03f1841e11fa0cb3b76154e95be15b7abe1dc0c5775451cf2bca4f870fe"},"schema_version":"1.0","source":{"id":"quant-ph/0407257","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0407257","created_at":"2026-07-04T16:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0407257v2","created_at":"2026-07-04T16:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0407257","created_at":"2026-07-04T16:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"WFFSQUAU572Y","created_at":"2026-07-04T16:50:22Z"},{"alias_kind":"pith_short_16","alias_value":"WFFSQUAU572YW6WE","created_at":"2026-07-04T16:50:22Z"},{"alias_kind":"pith_short_8","alias_value":"WFFSQUAU","created_at":"2026-07-04T16:50:22Z"}],"graph_snapshots":[{"event_id":"sha256:1eef0339e01155eb54677b61e761211cb35d6925054de1e78ba2c87eb482db8e","target":"graph","created_at":"2026-07-04T16:50:22Z","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/quant-ph/0407257/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group $G$ is developed in detail. Several New features are shown to arise which have no counterparts in the familiar Cartesian case. Notable among these is the notion of a `semiquantised phase space', a structure on which the Weyl symbols of operators turn out to be naturally defined and, figuratively speaking, located midway between the classical phase space $T^*G$ and the Hilbert space of square integrable functions on $G$. General expressions for the star product for Weyl symbols are presented and explicitly worked ou","authors_text":"Alessandro Zampini, G. Marmo, N. Mukunda, R.Simon, S. Chaturvedi","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2004-07-30T06:02:39Z","title":"Wigner-Weyl isomorphism for quantum mechanics on Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0407257","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":"sha256:191477e1fc07b91284b3d006507d79b91c32700b635a1b98dc3be507cdc941ae","target":"record","created_at":"2026-07-04T16:50:22Z","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":"289efcccaf66dd97cb1b73daa1692fadfd7e9db671f3585bd590b27a97fb5a5a","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-07-30T06:02:39Z","title_canon_sha256":"6142c03f1841e11fa0cb3b76154e95be15b7abe1dc0c5775451cf2bca4f870fe"},"schema_version":"1.0","source":{"id":"quant-ph/0407257","kind":"arxiv","version":2}},"canonical_sha256":"b14b285014eff58b7ac4cdfbbd2eb743b8586badeae4df29aaf2262e34806be7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b14b285014eff58b7ac4cdfbbd2eb743b8586badeae4df29aaf2262e34806be7","first_computed_at":"2026-07-04T16:50:22.312894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:50:22.312894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wkSXtChJTDmIbJegWE2Uwq+m/Uqfm2quIS4x6GRFsj2GfFfsTYFJAo/A9bDCKozTATX8gvfNj59JZKbfaLMJDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:50:22.313251Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0407257","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:191477e1fc07b91284b3d006507d79b91c32700b635a1b98dc3be507cdc941ae","sha256:1eef0339e01155eb54677b61e761211cb35d6925054de1e78ba2c87eb482db8e"],"state_sha256":"592acce5790e86538ec97abcc11904f8552d6efc5513f83f8a71982f8768ac97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xr0eBSoXBWG/Vtv5SEmV7rAixW+PmDWwXjo89dRG8jrsMJc7GDo40exrN74Umz5pi7ChVhB8FIl5P9JgKwO7BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T14:40:58.270058Z","bundle_sha256":"7edeb8e95b9e398426081e6bb7c4545b30c3c56c27fc65f3352206e929415515"}}