{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CPNZFLM6R34FRMEE4Q2W6DCFD3","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":"a7a8374155f8bb0783019a381feb4e4cf14cee23e7eef5c924adc77ec0bce13f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-24T14:26:11Z","title_canon_sha256":"14d27488743bb5b8c3afc14522e0746cd5f63999e485eec78f1208897ec38727"},"schema_version":"1.0","source":{"id":"1808.08156","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.08156","created_at":"2026-05-18T00:07:22Z"},{"alias_kind":"arxiv_version","alias_value":"1808.08156v1","created_at":"2026-05-18T00:07:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08156","created_at":"2026-05-18T00:07:22Z"},{"alias_kind":"pith_short_12","alias_value":"CPNZFLM6R34F","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CPNZFLM6R34FRMEE","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CPNZFLM6","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:74e8b95b4b80c75f13d527e00068f4361296ae6b6d945adf5b5cbddcac42c182","target":"graph","created_at":"2026-05-18T00:07:22Z","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 show that the d-dimensional Haar system H^d on the unit cube I^d is a Schauder basis in the classical Besov space B_{p,q,1}^s(I^d), 0<p<1, defined by first order differences in the limiting case s=d(1/p-1), if and only if 0<q\\le p. For d=1 and p<q, this settles the only open case in our 1979 paper [4], where the Schauder basis property of H in B_{p,q,1}^s(I) for 0<p<1 was left undecided. We also consider the Schauder basis property of H^d for the standard Besov spaces B_{p,q}^s(I^d) defined by Fourier-analytic methods in the limiting cases s=d(1/p-1) and s=1, complementing results by Triebe","authors_text":"Peter Oswald","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-24T14:26:11Z","title":"Haar system as Schauder basis in Besov spaces: The limiting cases for 0 < p <= 1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08156","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":"sha256:07f54d4c50aad0ce26925253c72033ccad442c82afd595b60dafca45ce3a9843","target":"record","created_at":"2026-05-18T00:07:22Z","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":"a7a8374155f8bb0783019a381feb4e4cf14cee23e7eef5c924adc77ec0bce13f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-24T14:26:11Z","title_canon_sha256":"14d27488743bb5b8c3afc14522e0746cd5f63999e485eec78f1208897ec38727"},"schema_version":"1.0","source":{"id":"1808.08156","kind":"arxiv","version":1}},"canonical_sha256":"13db92ad9e8ef858b084e4356f0c451eec2f04b23443d68f4d06e67641cf06ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13db92ad9e8ef858b084e4356f0c451eec2f04b23443d68f4d06e67641cf06ee","first_computed_at":"2026-05-18T00:07:22.268288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:22.268288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N0vEKRHQLsUv2Ffh7sAjKaENKU3GI4LotgopHZUeb479pz52ykYIzJpwlZ9Kiv7AkjGI5taIzLV9db8rZjgSDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:22.269017Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.08156","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07f54d4c50aad0ce26925253c72033ccad442c82afd595b60dafca45ce3a9843","sha256:74e8b95b4b80c75f13d527e00068f4361296ae6b6d945adf5b5cbddcac42c182"],"state_sha256":"7fa37d67036d5215ad0eb7b961038e5df3bcbc10101dbec85e20a7b651f4157b"}