{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5UPY72KERBOE2VRR52JNNP7MMH","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":"bf523e84c9ee26762df6a3d2b60a166c07b6f5cae16ae4fba4819f835c37864e","cross_cats_sorted":["math.FA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-03-03T16:44:06Z","title_canon_sha256":"099a222eb2b83f24d413831137e92e2ea76dc7ecd266a500a8f93b9020186a07"},"schema_version":"1.0","source":{"id":"1403.0483","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0483","created_at":"2026-05-18T02:27:58Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0483v2","created_at":"2026-05-18T02:27:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0483","created_at":"2026-05-18T02:27:58Z"},{"alias_kind":"pith_short_12","alias_value":"5UPY72KERBOE","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5UPY72KERBOE2VRR","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5UPY72KE","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:361aba65409920ff0b1f8e1fa68c9f90cab1672067affd7391fec0196909ec87","target":"graph","created_at":"2026-05-18T02:27:58Z","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 construct an explicit orthonormal basis of piecewise ${}_{i+1}F_{i}$ hypergeometric polynomials for the Alpert multiresolution analysis. The Fourier transform of each basis function is written in terms of ${}_2F_3$ hypergeometric functions. Moreover, the entries in the matrix equation connecting the wavelets with the scaling functions are shown to be balanced ${}_4 F_3$ hypergeometric functions evaluated at $1$, which allows to compute them recursively via three-term recurrence relations.\n  The above results lead to a variety of new interesting identities and orthogonality relations reminis","authors_text":"Jeffrey S. Geronimo, Plamen Iliev","cross_cats":["math.FA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-03-03T16:44:06Z","title":"A hypergeometric basis for the Alpert multiresolution analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0483","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:ede9e739b20ae25927c7bc9dcea777c7001fb12052d9320af8065be7213379e4","target":"record","created_at":"2026-05-18T02:27:58Z","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":"bf523e84c9ee26762df6a3d2b60a166c07b6f5cae16ae4fba4819f835c37864e","cross_cats_sorted":["math.FA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-03-03T16:44:06Z","title_canon_sha256":"099a222eb2b83f24d413831137e92e2ea76dc7ecd266a500a8f93b9020186a07"},"schema_version":"1.0","source":{"id":"1403.0483","kind":"arxiv","version":2}},"canonical_sha256":"ed1f8fe944885c4d5631ee92d6bfec61f69d0cfa848e2d7aed978d9fb98aa922","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed1f8fe944885c4d5631ee92d6bfec61f69d0cfa848e2d7aed978d9fb98aa922","first_computed_at":"2026-05-18T02:27:58.760628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:58.760628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wqgksl7QiK0oJEicexQW55HFObKsJHgJMPzhvvOMrby3U0e0PHmWvmVke/nYkPtIMnXjOxpHKzR5owAZRw2kDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:58.761213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0483","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ede9e739b20ae25927c7bc9dcea777c7001fb12052d9320af8065be7213379e4","sha256:361aba65409920ff0b1f8e1fa68c9f90cab1672067affd7391fec0196909ec87"],"state_sha256":"57811c882fe07c8d8f55e533eccc12d09139204f5a9bbfafb4a6fa06cbd7793f"}