{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2002:Q5R2I34UATT5MZLGHU5YVKL6YD","short_pith_number":"pith:Q5R2I34U","schema_version":"1.0","canonical_sha256":"8763a46f9404e7d665663d3b8aa97ec0ff9f4964f01cc05e609e8bba14edc9fb","source":{"kind":"arxiv","id":"quant-ph/0205041","version":1},"attestation_state":"computed","paper":{"title":"Wigner functions for curved spaces I: On hyperboloids","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"George S.Pogosyan, Kurt Bernardo Wolf, Miguel Angel Alonso","submitted_at":"2002-05-08T23:02:32Z","abstract_excerpt":"We propose a Wigner quasiprobability distribution function for Hamiltonian systems in spaces of constant curvature --in this paper on hyperboloids--, which returns the correct marginals and has the covariance of the Shapiro functions under SO(D,1) transformations. To the free systems obeying the Laplace-Beltrami equation on the hyperboloid, we add a conic-oscillator potential in the hyperbolic coordinate. As an example, we analyze the 1-dimensional case on a hyperbola branch, where this conic-oscillator is the Poschl-Teller potential. We present the analytical solutions and plot the computed r"},"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":"quant-ph/0205041","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2002-05-08T23:02:32Z","cross_cats_sorted":[],"title_canon_sha256":"4f9250949413297d7257da58ce5dc9138e8e41680c546775e5163fd9d1a53429","abstract_canon_sha256":"5159a84ae3413af0059ebeb551e1f1c426d34ccb5df8201099ff6a42d3340bde"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:01.923557Z","signature_b64":"wIundB56nMuEOzNpmIUIQ7KTt6sTzlmSrGbzwn2APWwrUtKjCeA2oZs035NR5n7z73dpwlaH5QvOJmxPd2sZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8763a46f9404e7d665663d3b8aa97ec0ff9f4964f01cc05e609e8bba14edc9fb","last_reissued_at":"2026-05-18T01:38:01.922970Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:01.922970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wigner functions for curved spaces I: On hyperboloids","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"George S.Pogosyan, Kurt Bernardo Wolf, Miguel Angel Alonso","submitted_at":"2002-05-08T23:02:32Z","abstract_excerpt":"We propose a Wigner quasiprobability distribution function for Hamiltonian systems in spaces of constant curvature --in this paper on hyperboloids--, which returns the correct marginals and has the covariance of the Shapiro functions under SO(D,1) transformations. To the free systems obeying the Laplace-Beltrami equation on the hyperboloid, we add a conic-oscillator potential in the hyperbolic coordinate. As an example, we analyze the 1-dimensional case on a hyperbola branch, where this conic-oscillator is the Poschl-Teller potential. We present the analytical solutions and plot the computed r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0205041","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0205041","created_at":"2026-05-18T01:38:01.923049+00:00"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0205041v1","created_at":"2026-05-18T01:38:01.923049+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0205041","created_at":"2026-05-18T01:38:01.923049+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q5R2I34UATT5","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q5R2I34UATT5MZLG","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q5R2I34U","created_at":"2026-05-18T12:25:51.375804+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/Q5R2I34UATT5MZLGHU5YVKL6YD","json":"https://pith.science/pith/Q5R2I34UATT5MZLGHU5YVKL6YD.json","graph_json":"https://pith.science/api/pith-number/Q5R2I34UATT5MZLGHU5YVKL6YD/graph.json","events_json":"https://pith.science/api/pith-number/Q5R2I34UATT5MZLGHU5YVKL6YD/events.json","paper":"https://pith.science/paper/Q5R2I34U"},"agent_actions":{"view_html":"https://pith.science/pith/Q5R2I34UATT5MZLGHU5YVKL6YD","download_json":"https://pith.science/pith/Q5R2I34UATT5MZLGHU5YVKL6YD.json","view_paper":"https://pith.science/paper/Q5R2I34U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=quant-ph/0205041&json=true","fetch_graph":"https://pith.science/api/pith-number/Q5R2I34UATT5MZLGHU5YVKL6YD/graph.json","fetch_events":"https://pith.science/api/pith-number/Q5R2I34UATT5MZLGHU5YVKL6YD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q5R2I34UATT5MZLGHU5YVKL6YD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q5R2I34UATT5MZLGHU5YVKL6YD/action/storage_attestation","attest_author":"https://pith.science/pith/Q5R2I34UATT5MZLGHU5YVKL6YD/action/author_attestation","sign_citation":"https://pith.science/pith/Q5R2I34UATT5MZLGHU5YVKL6YD/action/citation_signature","submit_replication":"https://pith.science/pith/Q5R2I34UATT5MZLGHU5YVKL6YD/action/replication_record"}},"created_at":"2026-05-18T01:38:01.923049+00:00","updated_at":"2026-05-18T01:38:01.923049+00:00"}