{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:AD6WLOV2EKZZCHGXYOH4WCOUOV","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":"dbbef3042d9f7e6f84b1b8f4b25640646dbdcfb2d88926e7efd7269d207a9556","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-01-07T17:54:12Z","title_canon_sha256":"f3b6a46d0e217f24a7d9a537905b3cbd78c0a7f6ab94eb414a3d607894f3c1b5"},"schema_version":"1.0","source":{"id":"2001.02636","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.02636","created_at":"2026-07-05T00:55:30Z"},{"alias_kind":"arxiv_version","alias_value":"2001.02636v2","created_at":"2026-07-05T00:55:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.02636","created_at":"2026-07-05T00:55:30Z"},{"alias_kind":"pith_short_12","alias_value":"AD6WLOV2EKZZ","created_at":"2026-07-05T00:55:30Z"},{"alias_kind":"pith_short_16","alias_value":"AD6WLOV2EKZZCHGX","created_at":"2026-07-05T00:55:30Z"},{"alias_kind":"pith_short_8","alias_value":"AD6WLOV2","created_at":"2026-07-05T00:55:30Z"}],"graph_snapshots":[{"event_id":"sha256:af9fbc85eed4f31981bf5538dcece865151c6e7205d7a1817f2680405b12e532","target":"graph","created_at":"2026-07-05T00:55:30Z","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/2001.02636/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the present paper, optimal quadrature formulas in the sense of Sard are constructed for numerical integration of the integral $\\int_a^be^{2\\pi i\\omega x}\\varphi(x)d x$ with $\\omega\\in \\mathbb{R}$ in the Sobolev space $L_2^{(m)}[a,b]$ of complex-valued functions which are square integrable with $m$-th order derivative. Here, using the discrete analogue of the differential operator $\\frac{d^{2m}}{d x^{2m}}$, the explicit formulas for optimal coefficients are obtained. The order of convergence of the obtained optimal quadrature formula is $O(h^m)$. As an application, we implement the filtered ","authors_text":"Abdullo R. Hayotov, Chang-Ock Lee, Kholmat M. Shadimetov, Soomin Jeon","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-01-07T17:54:12Z","title":"Optimal quadrature formulas for non-periodic functions in Sobolev space and its application to CT image reconstruction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.02636","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":"sha256:98eea7b2e7c196d52414330dde1ebcb59fe4e70ea744572936aa6c4c192e7d84","target":"record","created_at":"2026-07-05T00:55:30Z","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":"dbbef3042d9f7e6f84b1b8f4b25640646dbdcfb2d88926e7efd7269d207a9556","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-01-07T17:54:12Z","title_canon_sha256":"f3b6a46d0e217f24a7d9a537905b3cbd78c0a7f6ab94eb414a3d607894f3c1b5"},"schema_version":"1.0","source":{"id":"2001.02636","kind":"arxiv","version":2}},"canonical_sha256":"00fd65baba22b3911cd7c38fcb09d4754b610b165c65efd390eecb1028556ba1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00fd65baba22b3911cd7c38fcb09d4754b610b165c65efd390eecb1028556ba1","first_computed_at":"2026-07-05T00:55:30.212904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:55:30.212904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EuR7R1hhHXxRdzgC76igRKLxRZxz9TlG9DjfHzJQj7n6k/QA5piUfOWLryezAFF/8K1VHWid1d1VXQn7zdEhAg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:55:30.213303Z","signed_message":"canonical_sha256_bytes"},"source_id":"2001.02636","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98eea7b2e7c196d52414330dde1ebcb59fe4e70ea744572936aa6c4c192e7d84","sha256:af9fbc85eed4f31981bf5538dcece865151c6e7205d7a1817f2680405b12e532"],"state_sha256":"ca5ada7f7209fbeaf284c3de235c9cd9be902661f34a7c17ddaaff63350b11c6"}