{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:Z3VR347OH3HIZDZOTTGOABJRHF","short_pith_number":"pith:Z3VR347O","schema_version":"1.0","canonical_sha256":"ceeb1df3ee3ece8c8f2e9ccce00531397eb28a788f478d36a3154823cfdde47f","source":{"kind":"arxiv","id":"1206.4385","version":2},"attestation_state":"computed","paper":{"title":"Comment on \"Quantum phase for an arbitrary system with finite-dimensional Hilbert space\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"David T. Pegg, Michael J. W. Hall","submitted_at":"2012-06-20T05:29:44Z","abstract_excerpt":"A construction of covariant quantum phase observables, for Hamiltonians with a finite number of energy eigenvalues, has been recently given by D. Arsenovic et al. [Phys. Rev. A 85, 044103 (2012)]. For Hamiltonians generating periodic evolution, we show that this construction is just a simple rescaling of the known canonical 'time' or 'age' observable, with the period T rescaled to 2\\pi. Further, for Hamiltonians generating quasiperiodic evolution, we note that the construction leads to a phase observable having several undesirable features, including (i) having a trivially uniform probability "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1206.4385","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-06-20T05:29:44Z","cross_cats_sorted":[],"title_canon_sha256":"bc53f25f6c049d1a28405abfe087b0d356971aff99d4b18728708187083173f5","abstract_canon_sha256":"f043bd7c5ad494564d50e9bd496d4352127a5dbef0a013426251022b25a6c56d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:51.233869Z","signature_b64":"eTb/CY0IWtwbwGIlB5za2a//F1aVcDR3EEsKChsNLtQDpg+qCGaMEEc3Ep9mGvA+bzkVcsPyfdx+DWivZIscDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ceeb1df3ee3ece8c8f2e9ccce00531397eb28a788f478d36a3154823cfdde47f","last_reissued_at":"2026-05-18T03:40:51.233166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:51.233166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comment on \"Quantum phase for an arbitrary system with finite-dimensional Hilbert space\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"David T. Pegg, Michael J. W. Hall","submitted_at":"2012-06-20T05:29:44Z","abstract_excerpt":"A construction of covariant quantum phase observables, for Hamiltonians with a finite number of energy eigenvalues, has been recently given by D. Arsenovic et al. [Phys. Rev. A 85, 044103 (2012)]. For Hamiltonians generating periodic evolution, we show that this construction is just a simple rescaling of the known canonical 'time' or 'age' observable, with the period T rescaled to 2\\pi. Further, for Hamiltonians generating quasiperiodic evolution, we note that the construction leads to a phase observable having several undesirable features, including (i) having a trivially uniform probability "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4385","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1206.4385","created_at":"2026-05-18T03:40:51.233260+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.4385v2","created_at":"2026-05-18T03:40:51.233260+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4385","created_at":"2026-05-18T03:40:51.233260+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z3VR347OH3HI","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z3VR347OH3HIZDZO","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z3VR347O","created_at":"2026-05-18T12:27:30.460161+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z3VR347OH3HIZDZOTTGOABJRHF","json":"https://pith.science/pith/Z3VR347OH3HIZDZOTTGOABJRHF.json","graph_json":"https://pith.science/api/pith-number/Z3VR347OH3HIZDZOTTGOABJRHF/graph.json","events_json":"https://pith.science/api/pith-number/Z3VR347OH3HIZDZOTTGOABJRHF/events.json","paper":"https://pith.science/paper/Z3VR347O"},"agent_actions":{"view_html":"https://pith.science/pith/Z3VR347OH3HIZDZOTTGOABJRHF","download_json":"https://pith.science/pith/Z3VR347OH3HIZDZOTTGOABJRHF.json","view_paper":"https://pith.science/paper/Z3VR347O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.4385&json=true","fetch_graph":"https://pith.science/api/pith-number/Z3VR347OH3HIZDZOTTGOABJRHF/graph.json","fetch_events":"https://pith.science/api/pith-number/Z3VR347OH3HIZDZOTTGOABJRHF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z3VR347OH3HIZDZOTTGOABJRHF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z3VR347OH3HIZDZOTTGOABJRHF/action/storage_attestation","attest_author":"https://pith.science/pith/Z3VR347OH3HIZDZOTTGOABJRHF/action/author_attestation","sign_citation":"https://pith.science/pith/Z3VR347OH3HIZDZOTTGOABJRHF/action/citation_signature","submit_replication":"https://pith.science/pith/Z3VR347OH3HIZDZOTTGOABJRHF/action/replication_record"}},"created_at":"2026-05-18T03:40:51.233260+00:00","updated_at":"2026-05-18T03:40:51.233260+00:00"}