{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:2P35LSQMO3GSY22C5HDIVQ4THX","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":"4c4dfe4f1d32f13e0c390d8117176d91a8d583f9ad05d7a0ec5d3bf8c343e184","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-12-25T18:37:41Z","title_canon_sha256":"72b4ca9f551883ab421491f1be706ff1cbffa447c27d38f1988c2375f4a32726"},"schema_version":"1.0","source":{"id":"2212.12945","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.12945","created_at":"2026-07-05T05:28:15Z"},{"alias_kind":"arxiv_version","alias_value":"2212.12945v1","created_at":"2026-07-05T05:28:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.12945","created_at":"2026-07-05T05:28:15Z"},{"alias_kind":"pith_short_12","alias_value":"2P35LSQMO3GS","created_at":"2026-07-05T05:28:15Z"},{"alias_kind":"pith_short_16","alias_value":"2P35LSQMO3GSY22C","created_at":"2026-07-05T05:28:15Z"},{"alias_kind":"pith_short_8","alias_value":"2P35LSQM","created_at":"2026-07-05T05:28:15Z"}],"graph_snapshots":[{"event_id":"sha256:098da5cf1b6daad09bab2050c4d4389174fc09f4bb68af77bd8936a20c8b9819","target":"graph","created_at":"2026-07-05T05:28:15Z","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/2212.12945/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Tile B-splines in $\\mathbb{R}^d$ are defined as autoconvolutions of the indicators of tiles, which are special self-similar compact sets whose integer translates tile the space $\\mathbb{R}^d$. These functions are not piecewise-polynomial, however, being direct generalizations of classical B-splines, they enjoy many of their properties and have some advantages. In particular, the precise values of the H\\\"older exponents of the tile B-splines are computed in this work. They sometimes exceed the regularity of the classical B-splines. The orthonormal systems of wavelets based on the tile B-splines","authors_text":"Tatyana Zaitseva","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-12-25T18:37:41Z","title":"Multivariate tile B-splines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.12945","kind":"arxiv","version":1},"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:b7b6a0a03235059b1d24fe9741b748afc120b0e46694b148775ee38cbe7b9129","target":"record","created_at":"2026-07-05T05:28:15Z","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":"4c4dfe4f1d32f13e0c390d8117176d91a8d583f9ad05d7a0ec5d3bf8c343e184","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-12-25T18:37:41Z","title_canon_sha256":"72b4ca9f551883ab421491f1be706ff1cbffa447c27d38f1988c2375f4a32726"},"schema_version":"1.0","source":{"id":"2212.12945","kind":"arxiv","version":1}},"canonical_sha256":"d3f7d5ca0c76cd2c6b42e9c68ac3933dc931d6960e57af673346dc0408ba1f07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3f7d5ca0c76cd2c6b42e9c68ac3933dc931d6960e57af673346dc0408ba1f07","first_computed_at":"2026-07-05T05:28:15.029467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:28:15.029467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qZ6aUw2GTjKjC69HVB+A0F48ug6jghVL9HNg2N0MQFnsLEr4YDRkHX2L7lTLRjysz+E5QXKKemr5cIyTX4zUCg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:28:15.029812Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.12945","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7b6a0a03235059b1d24fe9741b748afc120b0e46694b148775ee38cbe7b9129","sha256:098da5cf1b6daad09bab2050c4d4389174fc09f4bb68af77bd8936a20c8b9819"],"state_sha256":"dc31d77090c13fbfbab5752684bae2985cbd3ded152d679a43a1c2c3592b0dd6"}