{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DJUO4ANGDNUXPSLIE5WUJQKFTV","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":"64d0ed3c02934a1ee7d0fd7e0ca1cbddf64710ef51cb98d62c909bcfe641129e","cross_cats_sorted":["math.NA","physics.data-an","physics.geo-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-07-29T14:24:50Z","title_canon_sha256":"b38c0ccd1e16e1c6da68c342087abaf6850827cc7d7a6d5da3118e3863d94d1b"},"schema_version":"1.0","source":{"id":"1007.5226","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.5226","created_at":"2026-05-18T04:24:27Z"},{"alias_kind":"arxiv_version","alias_value":"1007.5226v2","created_at":"2026-05-18T04:24:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.5226","created_at":"2026-05-18T04:24:27Z"},{"alias_kind":"pith_short_12","alias_value":"DJUO4ANGDNUX","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DJUO4ANGDNUXPSLI","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DJUO4ANG","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:e17c5887ee857ed89e811dd5f4c9fae16f4b80d43dd948f1fec415f347e1f5df","target":"graph","created_at":"2026-05-18T04:24:27Z","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 pose and solve the analogue of Slepian's time-frequency concentration problem in the two-dimensional plane, for applications in the natural sciences. We determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the plane, or, alternatively, of strictly spacelimited functions that are optimally concentrated in the Fourier domain. The Cartesian Slepian functions can be found by solving a Fredholm integral equation whose associated eigenvalues are a measure of the spatiospectral concentration. Both the spatial and spectral region","authors_text":"Dong V. Wang, Frederik J. Simons","cross_cats":["math.NA","physics.data-an","physics.geo-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-07-29T14:24:50Z","title":"Spatiospectral concentration in the Cartesian plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.5226","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:cf1a7bf4116d9efc451913b6f73c520621063bde1a58abc725a7f01b157a98f2","target":"record","created_at":"2026-05-18T04:24:27Z","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":"64d0ed3c02934a1ee7d0fd7e0ca1cbddf64710ef51cb98d62c909bcfe641129e","cross_cats_sorted":["math.NA","physics.data-an","physics.geo-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-07-29T14:24:50Z","title_canon_sha256":"b38c0ccd1e16e1c6da68c342087abaf6850827cc7d7a6d5da3118e3863d94d1b"},"schema_version":"1.0","source":{"id":"1007.5226","kind":"arxiv","version":2}},"canonical_sha256":"1a68ee01a61b6977c968276d44c1459d4828a3cd0742a771f927ca5dd6b22b58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a68ee01a61b6977c968276d44c1459d4828a3cd0742a771f927ca5dd6b22b58","first_computed_at":"2026-05-18T04:24:27.570649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:27.570649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UhF9ZKOsGscOTcuEbvm6YERDwWmJdyzzsl+8IfSbyyKt0I/kRORus5MZ7UtUkoOfgHQr4wphmu68gHsEcP8vCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:27.571415Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.5226","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf1a7bf4116d9efc451913b6f73c520621063bde1a58abc725a7f01b157a98f2","sha256:e17c5887ee857ed89e811dd5f4c9fae16f4b80d43dd948f1fec415f347e1f5df"],"state_sha256":"9fa73fadc60cd83aedefd47ee0d7d1539940818e831295f39897218d3045db1d"}