{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:V5G7XP7LPII3JPX7M55ET7WYVB","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":"734960ef6cf28aa2e7fd2106e0a93529d4c46b6e72a02c74691bee0823591f9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-10-01T16:42:06Z","title_canon_sha256":"9a7edabe768c4c8582ebb39a7601f55898431ba6bffc462e84fc2c144cc80d8a"},"schema_version":"1.0","source":{"id":"1410.0280","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0280","created_at":"2026-05-18T02:35:46Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0280v2","created_at":"2026-05-18T02:35:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0280","created_at":"2026-05-18T02:35:46Z"},{"alias_kind":"pith_short_12","alias_value":"V5G7XP7LPII3","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"V5G7XP7LPII3JPX7","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"V5G7XP7L","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:3cd828b9dd90c5db01158160ab84f1e1c6efa2dad44e3122aa431712463fb66b","target":"graph","created_at":"2026-05-18T02:35:46Z","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 here study Finite Impulse Response (FIR) rectangular, not necessarily causal, systems which are (para)-unitary on the unit circle (=the class $\\mathcal{U}$). First, we offer three characterizations of these systems. Then, introduce a %easy-to-use description of all FIRs in $\\mathcal{U}$, as copies of a real polytope, parametrized by the dimensions and the McMillan degree of the FIRs.\n  Finally, we present six simple ways (along with their combinations) to construct, from any FIR, a large family of FIRs, of various dimensions and McMillan degrees, so that whenever the original system is in $","authors_text":"Daniel Alpay, Izchak Lewkowicz, Palle Jorgensen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-10-01T16:42:06Z","title":"Characterizations of families of rectangular finite impulse response, para-unitary systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0280","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:d4da5b1b299b2c37fd4d87b4ca5612363ffc19f11174c2933bbfcee902efb998","target":"record","created_at":"2026-05-18T02:35:46Z","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":"734960ef6cf28aa2e7fd2106e0a93529d4c46b6e72a02c74691bee0823591f9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-10-01T16:42:06Z","title_canon_sha256":"9a7edabe768c4c8582ebb39a7601f55898431ba6bffc462e84fc2c144cc80d8a"},"schema_version":"1.0","source":{"id":"1410.0280","kind":"arxiv","version":2}},"canonical_sha256":"af4dfbbfeb7a11b4beff677a49fed8a86bf9c70420aca00d513e259905a2637a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af4dfbbfeb7a11b4beff677a49fed8a86bf9c70420aca00d513e259905a2637a","first_computed_at":"2026-05-18T02:35:46.895423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:46.895423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WCReDjalPyllBDiDkEsow6sNuDn7bam9Js9MzUbZRkfLWaPZqBKTw60h4gQFlVljbaEKjW4mrswvYonagbj4Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:46.895836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0280","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4da5b1b299b2c37fd4d87b4ca5612363ffc19f11174c2933bbfcee902efb998","sha256:3cd828b9dd90c5db01158160ab84f1e1c6efa2dad44e3122aa431712463fb66b"],"state_sha256":"1df372d078732721e5c2a2a168ae68add8736b8fe2f4bd4fcb22ea6cd4176839"}