{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4VPAZFEGD3HHTFTHPAKMKXFAAV","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":"09ad3fff9052761793760af798adb89cc76b745dfa19860127f06962ff7e8cba","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-28T16:58:36Z","title_canon_sha256":"ba327d56397c6174d8880ea2b199225fd15a09c0bd7245a3632f9d5e71c1643c"},"schema_version":"1.0","source":{"id":"1708.08421","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.08421","created_at":"2026-05-18T00:36:36Z"},{"alias_kind":"arxiv_version","alias_value":"1708.08421v1","created_at":"2026-05-18T00:36:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08421","created_at":"2026-05-18T00:36:36Z"},{"alias_kind":"pith_short_12","alias_value":"4VPAZFEGD3HH","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4VPAZFEGD3HHTFTH","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4VPAZFEG","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:4979ec208f5c0381af3f8db29451f4434c01ca181c37a1b5e70df6c81a169671","target":"graph","created_at":"2026-05-18T00:36:36Z","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"},"paper":{"abstract_excerpt":"To effectively capture singularities in high-dimensional data and functions, multivariate compactly supported tight framelets, having directionality and derived from refinable box splines, are of particular interest in both theory and applications. The $d$-dimensional Haar refinable function $\\chi_{[0,1]^d}$ is a simple example of refinable box splines. For every dimension $d\\in \\N$, in this paper we construct a directional compactly supported $d$-dimensional Haar tight framelet such that all its high-pass filters in its underlying tight framelet filter bank have only two nonzero coefficients ","authors_text":"Bin Han, Tao Li, Xiaosheng Zhuang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-28T16:58:36Z","title":"Directional Compactly supported Box Spline Tight Framelets with Simple Structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08421","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":"sha256:6b44b397d594f9ac59ae203da3d5c25f11f49eeeb5e8b0ef010ed130397693d1","target":"record","created_at":"2026-05-18T00:36:36Z","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":"09ad3fff9052761793760af798adb89cc76b745dfa19860127f06962ff7e8cba","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-28T16:58:36Z","title_canon_sha256":"ba327d56397c6174d8880ea2b199225fd15a09c0bd7245a3632f9d5e71c1643c"},"schema_version":"1.0","source":{"id":"1708.08421","kind":"arxiv","version":1}},"canonical_sha256":"e55e0c94861ece7996677814c55ca005634cc2e4232632a678f418c01ec3095d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e55e0c94861ece7996677814c55ca005634cc2e4232632a678f418c01ec3095d","first_computed_at":"2026-05-18T00:36:36.081208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:36.081208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VrWi+MNtmMGCEcJoAtHnFAoC3d6pHYeTVBQ3uTlhGzt+6XOWWDKSs9z4DieTpDcf64/1cGjPKoysO8+j64UpAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:36.081810Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.08421","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b44b397d594f9ac59ae203da3d5c25f11f49eeeb5e8b0ef010ed130397693d1","sha256:4979ec208f5c0381af3f8db29451f4434c01ca181c37a1b5e70df6c81a169671"],"state_sha256":"bea1001cf4d2e03b0ee1583181f915c690354737ae624e168cf2da5b5fa6e275"}