{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EMQJTDROVF54CSSUQZX2USYRX7","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":"ad203323193b3192c1fe192d799671a25a7f569e17d5627b4224a02f6a7e1876","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-07-11T22:58:49Z","title_canon_sha256":"be62e9a3a628a7464605308b7390f5af3b38f063e12f3594bdc3d0ef1edb4a4a"},"schema_version":"1.0","source":{"id":"1507.03167","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03167","created_at":"2026-05-18T00:57:04Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03167v2","created_at":"2026-05-18T00:57:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03167","created_at":"2026-05-18T00:57:04Z"},{"alias_kind":"pith_short_12","alias_value":"EMQJTDROVF54","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EMQJTDROVF54CSSU","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EMQJTDRO","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:28a462e9d73083760a402fefb844f4c3b8703e89595eefe4133575adb411f192","target":"graph","created_at":"2026-05-18T00:57:04Z","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":"We study the Weyl-Wigner transform in the case of discrete variables defined in a Hilbert space of finite prime-number dimensionality $N$. We define a family of Weyl-Wigner transforms as function of a phase parameter. We show that it is only for a specific value of the parameter that all the properties we have examined have a parallel with the case of continuous variables defined in an infinite-dimensional Hilbert space. A geometrical interpretation is briefly discussed.","authors_text":"Ady Mann, Michael Revzen, Pier A. Mello","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-07-11T22:58:49Z","title":"A Family of Weyl-Wigner Transforms for Discrete Variables Defined in a Finite-Dimensional Hilbert Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03167","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:f8ec981046bcd524353902e45674bf89d73a798c9888c022d4ef0a45667cec0c","target":"record","created_at":"2026-05-18T00:57:04Z","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":"ad203323193b3192c1fe192d799671a25a7f569e17d5627b4224a02f6a7e1876","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-07-11T22:58:49Z","title_canon_sha256":"be62e9a3a628a7464605308b7390f5af3b38f063e12f3594bdc3d0ef1edb4a4a"},"schema_version":"1.0","source":{"id":"1507.03167","kind":"arxiv","version":2}},"canonical_sha256":"2320998e2ea97bc14a54866faa4b11bfe6d59112a0e70abc2161ed9600a74515","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2320998e2ea97bc14a54866faa4b11bfe6d59112a0e70abc2161ed9600a74515","first_computed_at":"2026-05-18T00:57:04.923626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:04.923626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uL8z3xZAQc5rQNCGG3+ygI9IWr6T7ayMib1PSA48gIwdtSzFYJr2tLu3fXX6oJTAbuyljadWUfbDCyLGSPvCDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:04.924175Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.03167","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8ec981046bcd524353902e45674bf89d73a798c9888c022d4ef0a45667cec0c","sha256:28a462e9d73083760a402fefb844f4c3b8703e89595eefe4133575adb411f192"],"state_sha256":"a7fd6c300af939b8ac3bd3f73b7ffcef24d1739384a4650690590ae68f4fdaff"}