{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PULEQPFU6KP3EGI22B2PKT3SIQ","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":"d25720b00a127afd10761df507281bc05ce163ca7e2a52d6108588a11470fe52","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"quant-ph","submitted_at":"2024-05-08T15:54:35Z","title_canon_sha256":"48b8138e3258da68ff51beab141c738e1b3dc553cdb215c1260a18d66add6059"},"schema_version":"1.0","source":{"id":"2405.05163","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.05163","created_at":"2026-07-05T08:17:05Z"},{"alias_kind":"arxiv_version","alias_value":"2405.05163v1","created_at":"2026-07-05T08:17:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.05163","created_at":"2026-07-05T08:17:05Z"},{"alias_kind":"pith_short_12","alias_value":"PULEQPFU6KP3","created_at":"2026-07-05T08:17:05Z"},{"alias_kind":"pith_short_16","alias_value":"PULEQPFU6KP3EGI2","created_at":"2026-07-05T08:17:05Z"},{"alias_kind":"pith_short_8","alias_value":"PULEQPFU","created_at":"2026-07-05T08:17:05Z"}],"graph_snapshots":[{"event_id":"sha256:ba702e0ae4c9b482da3893b56918777cdd4ac3fc4b02fa3789486cdcc2a2f4a3","target":"graph","created_at":"2026-07-05T08:17:05Z","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/2405.05163/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Two methods for fast Fourier transforms are used in a quantum context. The first method is for systems with dimension of the Hilbert space $D=d^n$ with $d$ an odd integer, and is inspired by the Cooley-Tukey formalism. The `large Fourier transform' is expressed as a sequence of $n$ `small Fourier transforms' (together with some other transforms) in quantum systems with $d$-dimensional Hilbert space. Limitations of the method are discussed. In some special cases, the $n$ Fourier transforms can be performed in parallel. The second method is for systems with dimension of the Hilbert space $D=d_0.","authors_text":"A. Vourdas, C. Lei","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"quant-ph","submitted_at":"2024-05-08T15:54:35Z","title":"Fast Fourier transforms and fast Wigner and Weyl functions in large quantum systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.05163","kind":"arxiv","version":1},"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":"sha256:1eac932a91ce2a89bc5687102d1d73306428e915b8cfcf695ba90892c349b3d2","target":"record","created_at":"2026-07-05T08:17:05Z","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":"d25720b00a127afd10761df507281bc05ce163ca7e2a52d6108588a11470fe52","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"quant-ph","submitted_at":"2024-05-08T15:54:35Z","title_canon_sha256":"48b8138e3258da68ff51beab141c738e1b3dc553cdb215c1260a18d66add6059"},"schema_version":"1.0","source":{"id":"2405.05163","kind":"arxiv","version":1}},"canonical_sha256":"7d16483cb4f29fb2191ad074f54f724413ba508807fc64047047b49d9dbd7f47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d16483cb4f29fb2191ad074f54f724413ba508807fc64047047b49d9dbd7f47","first_computed_at":"2026-07-05T08:17:05.809503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:17:05.809503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YU+BjXx5bQRy9WZjF8mlrjT+gUpZ83ltKlTrEczOy7+qzq9cWq65OBeLtQCd/5/dhnTDzFyL9Sh52GtAkkNNBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:17:05.809928Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.05163","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1eac932a91ce2a89bc5687102d1d73306428e915b8cfcf695ba90892c349b3d2","sha256:ba702e0ae4c9b482da3893b56918777cdd4ac3fc4b02fa3789486cdcc2a2f4a3"],"state_sha256":"cee2ecb85123e7099cbf7f883924f7b2e800f3b2b3abca24a8c81566657c2257"}