{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:F4AM6GNJRPDEV4UF3BWOS2MNBV","short_pith_number":"pith:F4AM6GNJ","schema_version":"1.0","canonical_sha256":"2f00cf19a98bc64af285d86ce9698d0d4f25907987f38f4b2efe7a1b44050005","source":{"kind":"arxiv","id":"2111.07182","version":3},"attestation_state":"computed","paper":{"title":"Density theorems with applications in quantum signal processing","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.CA","authors_text":"Rahul Sarkar, Theodore J. Yoder","submitted_at":"2021-11-13T20:00:21Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2111.07182","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2021-11-13T20:00:21Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"d06507e61d3fa02e492edc379f86c8a846592d248f88cf811bfceaa3fe1d1873","abstract_canon_sha256":"309dbf0ecc86c9af811738d5eb8f0ada4747aef67b42d8c6a72d5efd0ca5a62f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:12:36.911626Z","signature_b64":"ZUfOWWfrICTMv6a6WgubYAvFvog9jVzNGsH5l2N5tgb1JMwmf9r03plHCgt8Xi+TmcyxcCIkkDpLXVHMA7LtBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f00cf19a98bc64af285d86ce9698d0d4f25907987f38f4b2efe7a1b44050005","last_reissued_at":"2026-07-05T04:12:36.911223Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:12:36.911223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Density theorems with applications in quantum signal processing","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.CA","authors_text":"Rahul Sarkar, Theodore J. Yoder","submitted_at":"2021-11-13T20:00:21Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.07182","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.07182/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2111.07182","created_at":"2026-07-05T04:12:36.911278+00:00"},{"alias_kind":"arxiv_version","alias_value":"2111.07182v3","created_at":"2026-07-05T04:12:36.911278+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.07182","created_at":"2026-07-05T04:12:36.911278+00:00"},{"alias_kind":"pith_short_12","alias_value":"F4AM6GNJRPDE","created_at":"2026-07-05T04:12:36.911278+00:00"},{"alias_kind":"pith_short_16","alias_value":"F4AM6GNJRPDEV4UF","created_at":"2026-07-05T04:12:36.911278+00:00"},{"alias_kind":"pith_short_8","alias_value":"F4AM6GNJ","created_at":"2026-07-05T04:12:36.911278+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/F4AM6GNJRPDEV4UF3BWOS2MNBV","json":"https://pith.science/pith/F4AM6GNJRPDEV4UF3BWOS2MNBV.json","graph_json":"https://pith.science/api/pith-number/F4AM6GNJRPDEV4UF3BWOS2MNBV/graph.json","events_json":"https://pith.science/api/pith-number/F4AM6GNJRPDEV4UF3BWOS2MNBV/events.json","paper":"https://pith.science/paper/F4AM6GNJ"},"agent_actions":{"view_html":"https://pith.science/pith/F4AM6GNJRPDEV4UF3BWOS2MNBV","download_json":"https://pith.science/pith/F4AM6GNJRPDEV4UF3BWOS2MNBV.json","view_paper":"https://pith.science/paper/F4AM6GNJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2111.07182&json=true","fetch_graph":"https://pith.science/api/pith-number/F4AM6GNJRPDEV4UF3BWOS2MNBV/graph.json","fetch_events":"https://pith.science/api/pith-number/F4AM6GNJRPDEV4UF3BWOS2MNBV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F4AM6GNJRPDEV4UF3BWOS2MNBV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F4AM6GNJRPDEV4UF3BWOS2MNBV/action/storage_attestation","attest_author":"https://pith.science/pith/F4AM6GNJRPDEV4UF3BWOS2MNBV/action/author_attestation","sign_citation":"https://pith.science/pith/F4AM6GNJRPDEV4UF3BWOS2MNBV/action/citation_signature","submit_replication":"https://pith.science/pith/F4AM6GNJRPDEV4UF3BWOS2MNBV/action/replication_record"}},"created_at":"2026-07-05T04:12:36.911278+00:00","updated_at":"2026-07-05T04:12:36.911278+00:00"}