{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QLIUMSQRYUM3OMS6GVE4BHF2XW","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":"64197b02bff5951eae7cc38b7c1a5d131677db5fa02a7d7f01d1b6e0e029b4a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-15T13:36:09Z","title_canon_sha256":"d5917d4f642d984cf09ba3e3aa1ceb3e526574e1e4946e634392ae1312dc40b8"},"schema_version":"1.0","source":{"id":"1302.3751","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3751","created_at":"2026-05-18T03:33:35Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3751v1","created_at":"2026-05-18T03:33:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3751","created_at":"2026-05-18T03:33:35Z"},{"alias_kind":"pith_short_12","alias_value":"QLIUMSQRYUM3","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QLIUMSQRYUM3OMS6","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QLIUMSQR","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:31b7dbba1f48c4960a2d56637cc65a30196a8c2592616e7427ba0442cd973e0a","target":"graph","created_at":"2026-05-18T03:33:35Z","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":"Nowadays the theory and application of wavelet decompositions plays an important role not only for the study of function spaces (of Lebesgue, Hardy, Sobolev, Besov, Triebel-Lizorkin type) but also for its applications in signal and numerical analysis, partial differential equations and image processing. In this context it it a hard problem to construct wavelet bases for suitable function spaces on domains, e. g. the unit cube. A big step in this direction are the contributions of Hans Triebel from 2006 to 2008 where he constructed Riesz bases for classes of Besov- and Triebel-Lizorkin spaces o","authors_text":"Benjamin Scharf","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-15T13:36:09Z","title":"Wavelets in function spaces on cellular domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3751","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:a2ee06f9079852d39f8288758ccc423173e3d92976be9c055e8277132ca48bf0","target":"record","created_at":"2026-05-18T03:33:35Z","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":"64197b02bff5951eae7cc38b7c1a5d131677db5fa02a7d7f01d1b6e0e029b4a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-15T13:36:09Z","title_canon_sha256":"d5917d4f642d984cf09ba3e3aa1ceb3e526574e1e4946e634392ae1312dc40b8"},"schema_version":"1.0","source":{"id":"1302.3751","kind":"arxiv","version":1}},"canonical_sha256":"82d1464a11c519b7325e3549c09cbabdbed2e54e7fa8c45594fcd9387493ec56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82d1464a11c519b7325e3549c09cbabdbed2e54e7fa8c45594fcd9387493ec56","first_computed_at":"2026-05-18T03:33:35.872008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:35.872008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wYV+LyFSwp3sh6u9TRtSXg6vMLqX+zRomn/3iJQMd/sGmcrSgIKgiuShataHhd6kxGhGtA1I3Wa3elisoMDrCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:35.873071Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3751","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2ee06f9079852d39f8288758ccc423173e3d92976be9c055e8277132ca48bf0","sha256:31b7dbba1f48c4960a2d56637cc65a30196a8c2592616e7427ba0442cd973e0a"],"state_sha256":"61a3deb49a0caba973ca78232b8fb0945a60bb8fa3e43bb0fa6443e49ab4d5e6"}