{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7YNKXRHNNJA6B4FSBSJXIUBIL3","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":"9820a5234927118b0d87da05838ec5f755be7c00773e78f023b50e0fb36c9581","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-20T12:41:56Z","title_canon_sha256":"3816272e647e64fbb234d32d9596a1eafde2248c3087dc34edc2234212b23262"},"schema_version":"1.0","source":{"id":"1707.06477","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06477","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06477v1","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06477","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"7YNKXRHNNJA6","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7YNKXRHNNJA6B4FS","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7YNKXRHN","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:37d406bea246ed25c3bfc1d3ad459ac4775e65cc72da592ffb32536b1f68af13","target":"graph","created_at":"2026-05-18T00:39:53Z","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 give a new characterization of Nikolskii-Besov classes of functions of fractional smoothness by means of a nonlinear integration by parts formula in the form of a nonlinear inequality. A similar characterization is obtained for Nikolskii-Besov classes with respect to Gaussian measures on finite- and infinite-dimensional spaces.","authors_text":"Egor D. Kosov, Svetlana N. Popova, Vladimir I. Bogachev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-20T12:41:56Z","title":"A new approach to Nikolskii-Besov classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06477","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":"sha256:37f917bae2c4bb503c3ab4f08abfabd1d6b090f2f23463280be3baa1003d9f18","target":"record","created_at":"2026-05-18T00:39:53Z","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":"9820a5234927118b0d87da05838ec5f755be7c00773e78f023b50e0fb36c9581","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-20T12:41:56Z","title_canon_sha256":"3816272e647e64fbb234d32d9596a1eafde2248c3087dc34edc2234212b23262"},"schema_version":"1.0","source":{"id":"1707.06477","kind":"arxiv","version":1}},"canonical_sha256":"fe1aabc4ed6a41e0f0b20c937450285ede35ef9ce590f6cff585b664f320aa74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe1aabc4ed6a41e0f0b20c937450285ede35ef9ce590f6cff585b664f320aa74","first_computed_at":"2026-05-18T00:39:53.715522Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:53.715522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wkj6U3c0ziBTcNpafxyvDqgups91rEfkUtMTMzE1GiW90nNel54C/ErmcWRt67Zgk0NTIOFA8xCN5PPkdGfFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:53.716212Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.06477","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37f917bae2c4bb503c3ab4f08abfabd1d6b090f2f23463280be3baa1003d9f18","sha256:37d406bea246ed25c3bfc1d3ad459ac4775e65cc72da592ffb32536b1f68af13"],"state_sha256":"32b9f548d8481ffbd2ff5f2bfe7a59ede97fa0c3685b19cad875a6f118cfcddb"}