{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4VPAZFEGD3HHTFTHPAKMKXFAAV","short_pith_number":"pith:4VPAZFEG","canonical_record":{"source":{"id":"1708.08421","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-28T16:58:36Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ba327d56397c6174d8880ea2b199225fd15a09c0bd7245a3632f9d5e71c1643c","abstract_canon_sha256":"09ad3fff9052761793760af798adb89cc76b745dfa19860127f06962ff7e8cba"},"schema_version":"1.0"},"canonical_sha256":"e55e0c94861ece7996677814c55ca005634cc2e4232632a678f418c01ec3095d","source":{"kind":"arxiv","id":"1708.08421","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4VPAZFEGD3HHTFTHPAKMKXFAAV","target":"record","payload":{"canonical_record":{"source":{"id":"1708.08421","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-08-28T16:58:36Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ba327d56397c6174d8880ea2b199225fd15a09c0bd7245a3632f9d5e71c1643c","abstract_canon_sha256":"09ad3fff9052761793760af798adb89cc76b745dfa19860127f06962ff7e8cba"},"schema_version":"1.0"},"canonical_sha256":"e55e0c94861ece7996677814c55ca005634cc2e4232632a678f418c01ec3095d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:36.081810Z","signature_b64":"VrWi+MNtmMGCEcJoAtHnFAoC3d6pHYeTVBQ3uTlhGzt+6XOWWDKSs9z4DieTpDcf64/1cGjPKoysO8+j64UpAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e55e0c94861ece7996677814c55ca005634cc2e4232632a678f418c01ec3095d","last_reissued_at":"2026-05-18T00:36:36.081208Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:36.081208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.08421","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4atUY2jaIry59OCuplQD+fWeAJkpzRlSvu411jm64HKKjKYpShBO9MMoGy6DG/h7i0FOytmkhYIA/8U4foQnAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:32:57.309110Z"},"content_sha256":"6b44b397d594f9ac59ae203da3d5c25f11f49eeeb5e8b0ef010ed130397693d1","schema_version":"1.0","event_id":"sha256:6b44b397d594f9ac59ae203da3d5c25f11f49eeeb5e8b0ef010ed130397693d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4VPAZFEGD3HHTFTHPAKMKXFAAV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Directional Compactly supported Box Spline Tight Framelets with Simple Structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Bin Han, Tao Li, Xiaosheng Zhuang","submitted_at":"2017-08-28T16:58:36Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08421","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RvJW0TYxYcZDbKOlDUm6h2IyXYANSIwIeHy5oy6R0d/wq5naYEFI0b2Ci2YHSjJiwcJdjsS5zzEYH+QoPuRNDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:32:57.309490Z"},"content_sha256":"4979ec208f5c0381af3f8db29451f4434c01ca181c37a1b5e70df6c81a169671","schema_version":"1.0","event_id":"sha256:4979ec208f5c0381af3f8db29451f4434c01ca181c37a1b5e70df6c81a169671"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4VPAZFEGD3HHTFTHPAKMKXFAAV/bundle.json","state_url":"https://pith.science/pith/4VPAZFEGD3HHTFTHPAKMKXFAAV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4VPAZFEGD3HHTFTHPAKMKXFAAV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T14:32:57Z","links":{"resolver":"https://pith.science/pith/4VPAZFEGD3HHTFTHPAKMKXFAAV","bundle":"https://pith.science/pith/4VPAZFEGD3HHTFTHPAKMKXFAAV/bundle.json","state":"https://pith.science/pith/4VPAZFEGD3HHTFTHPAKMKXFAAV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4VPAZFEGD3HHTFTHPAKMKXFAAV/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"owiti72UPLlJo6CDlFdxEBd/zZE41hIXLp5+Px87xQxBx0tidFoLZBi/xBw2pdLBs8ZC8PqI08K4HNexIb0LBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:32:57.312007Z","bundle_sha256":"0caf904d34f577e95afe2935cfabb3b4bbe309deb18ae196f4b63914fa8e9962"}}