{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:F4AM6GNJRPDEV4UF3BWOS2MNBV","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":"309dbf0ecc86c9af811738d5eb8f0ada4747aef67b42d8c6a72d5efd0ca5a62f","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2021-11-13T20:00:21Z","title_canon_sha256":"d06507e61d3fa02e492edc379f86c8a846592d248f88cf811bfceaa3fe1d1873"},"schema_version":"1.0","source":{"id":"2111.07182","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.07182","created_at":"2026-07-05T04:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"2111.07182v3","created_at":"2026-07-05T04:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.07182","created_at":"2026-07-05T04:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"F4AM6GNJRPDE","created_at":"2026-07-05T04:12:36Z"},{"alias_kind":"pith_short_16","alias_value":"F4AM6GNJRPDEV4UF","created_at":"2026-07-05T04:12:36Z"},{"alias_kind":"pith_short_8","alias_value":"F4AM6GNJ","created_at":"2026-07-05T04:12:36Z"}],"graph_snapshots":[{"event_id":"sha256:0c2b596d1618cc0dd0a89d18568d7c2d1efff06f4bbe351beb642adcc6035c5c","target":"graph","created_at":"2026-07-05T04:12:36Z","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/2111.07182/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the approximation capabilities of two families of univariate polynomials that arise in applications of quantum signal processing. Although approximation only in the domain $[0,1]$ is physically desired, these polynomial families are defined by bound constraints not just in $[0,1]$, but also with additional bound constraints outside $[0,1]$. One might wonder then if these additional constraints inhibit their approximation properties within $[0,1]$. The main result of this paper is that this is not the case -- the additional constraints do not hinder the ability of these polynomial fami","authors_text":"Rahul Sarkar, Theodore J. Yoder","cross_cats":["quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2021-11-13T20:00:21Z","title":"Density theorems with applications in quantum signal processing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.07182","kind":"arxiv","version":3},"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":"sha256:4e9965ea1206f83583812045095b42b70b4f4446bd1d1485150c59d55b19c676","target":"record","created_at":"2026-07-05T04:12:36Z","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":"309dbf0ecc86c9af811738d5eb8f0ada4747aef67b42d8c6a72d5efd0ca5a62f","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2021-11-13T20:00:21Z","title_canon_sha256":"d06507e61d3fa02e492edc379f86c8a846592d248f88cf811bfceaa3fe1d1873"},"schema_version":"1.0","source":{"id":"2111.07182","kind":"arxiv","version":3}},"canonical_sha256":"2f00cf19a98bc64af285d86ce9698d0d4f25907987f38f4b2efe7a1b44050005","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f00cf19a98bc64af285d86ce9698d0d4f25907987f38f4b2efe7a1b44050005","first_computed_at":"2026-07-05T04:12:36.911223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:12:36.911223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZUfOWWfrICTMv6a6WgubYAvFvog9jVzNGsH5l2N5tgb1JMwmf9r03plHCgt8Xi+TmcyxcCIkkDpLXVHMA7LtBw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:12:36.911626Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.07182","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e9965ea1206f83583812045095b42b70b4f4446bd1d1485150c59d55b19c676","sha256:0c2b596d1618cc0dd0a89d18568d7c2d1efff06f4bbe351beb642adcc6035c5c"],"state_sha256":"30a30c9ef49f0bd89999f11ce249d8b3dfaf6df972e35818e2d23c4cfbd5ba87"}