{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WMTKX772AFAOZD5BHZENJMQYQV","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":"e346506856e4b2e0d13299b4c94c13c49b487cef2027825030724d1915b30b2b","cross_cats_sorted":["astro-ph.GA","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-02-01T10:29:54Z","title_canon_sha256":"89b78d90a8f9fd7a32c2c5d9c09d97e6c6fc04bdcd3356b9ff29c8c3119bb791"},"schema_version":"1.0","source":{"id":"2602.01141","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.01141","created_at":"2026-07-08T01:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"2602.01141v2","created_at":"2026-07-08T01:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.01141","created_at":"2026-07-08T01:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"WMTKX772AFAO","created_at":"2026-07-08T01:18:25Z"},{"alias_kind":"pith_short_16","alias_value":"WMTKX772AFAOZD5B","created_at":"2026-07-08T01:18:25Z"},{"alias_kind":"pith_short_8","alias_value":"WMTKX772","created_at":"2026-07-08T01:18:25Z"}],"graph_snapshots":[{"event_id":"sha256:a0a17bccee95477380fac0a50435091b13af9ce0866c3018f87f747383c0b9d8","target":"graph","created_at":"2026-07-08T01:18:25Z","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/2602.01141/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We extend shapelets for the analysis of astronomical images to be available in a phase space, introducing \\textit{Wigner function shapelets}(WFSs). Whereas conventional shapelets expand images separately in configuration or Fourier space using Hermite-Gaussian or Laguerre-Gaussian modes, WFSs represent images directly in the four-dimensional phase space with symplectic group $\\mathrm{Sp}(4,\\mathbb{R})$, which is quantized by a phase-space cell $2\\pi\\lambdabar$ that determines a resolution limit of a telescope. WFSs consist of a bilinear form of the cross-Wigner function of the Laguerre-Gaussia","authors_text":"Shun Arai","cross_cats":["astro-ph.GA","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-02-01T10:29:54Z","title":"Wigner function shapelets: Symplectic representation of astronomical images"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.01141","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:ca0c3c790dd5ca5f5d5cff6f203e4c77aebd26588ee8961018bb2c8f39903dcb","target":"record","created_at":"2026-07-08T01:18:25Z","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":"e346506856e4b2e0d13299b4c94c13c49b487cef2027825030724d1915b30b2b","cross_cats_sorted":["astro-ph.GA","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-02-01T10:29:54Z","title_canon_sha256":"89b78d90a8f9fd7a32c2c5d9c09d97e6c6fc04bdcd3356b9ff29c8c3119bb791"},"schema_version":"1.0","source":{"id":"2602.01141","kind":"arxiv","version":2}},"canonical_sha256":"b326abfffa0140ec8fa13e48d4b21885793ddd9b13ed37e433f1413cd7b31aed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b326abfffa0140ec8fa13e48d4b21885793ddd9b13ed37e433f1413cd7b31aed","first_computed_at":"2026-07-08T01:18:25.003365Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-08T01:18:25.003365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s4MoXuoHGjFhX23mhXflS7b2+ZO5e93+CiIU/IlmEE4lejLmSFjNOefZApYwB4mWvM9oMus8iVXAuHcu3dqaAg==","signature_status":"signed_v1","signed_at":"2026-07-08T01:18:25.006779Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.01141","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca0c3c790dd5ca5f5d5cff6f203e4c77aebd26588ee8961018bb2c8f39903dcb","sha256:a0a17bccee95477380fac0a50435091b13af9ce0866c3018f87f747383c0b9d8"],"state_sha256":"25e0d5161f4c9cb0bc627c00d82fe7e00019b428a4ccb72ea95d8967529808d7"}