{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PVAKETLCRV3L4UXOMRIT5F6BBS","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":"4caea43c96a218a9712af915b12231a9994b7dd025e217b7019181ff81cd3d14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-15T12:48:10Z","title_canon_sha256":"274fa94b309f0d31fb048e9232c3fb12fcc51742d4c469e53db12b6876ccaa5a"},"schema_version":"1.0","source":{"id":"1811.07704","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.07704","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"arxiv_version","alias_value":"1811.07704v1","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07704","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"pith_short_12","alias_value":"PVAKETLCRV3L","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PVAKETLCRV3L4UXO","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PVAKETLC","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:47b32a0cde99f13a0b2a179aec57a9a02139f885a9fd19ff44848a508fbac14d","target":"graph","created_at":"2026-05-18T00:00:23Z","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":"In this paper we establish approximation properties of Ces\\`{a}ro $(C,-\\alpha )$ means with $\\alpha$ $\\epsilon$ $(0,1)$ of Vilenkin-Fourier series.This result allows one to obtain a condition which is sufficient for the convergence of the means $\\sigma_n^{-\\alpha }(f,x)$ to $f(x)$ in the $L^p-$metric.","authors_text":"Tsitsino Tepnadze","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-15T12:48:10Z","title":"On the Approximation Properties of Ces\\`{a}ro Means of Negative Order of Vilenkin-Fourier Series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07704","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:e3be8187a6744a0bb5825a71a9efd91bb6191e8bbe41c4f1521a25ec059dfd17","target":"record","created_at":"2026-05-18T00:00:23Z","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":"4caea43c96a218a9712af915b12231a9994b7dd025e217b7019181ff81cd3d14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-15T12:48:10Z","title_canon_sha256":"274fa94b309f0d31fb048e9232c3fb12fcc51742d4c469e53db12b6876ccaa5a"},"schema_version":"1.0","source":{"id":"1811.07704","kind":"arxiv","version":1}},"canonical_sha256":"7d40a24d628d76be52ee64513e97c10cb1942d936da2ee27bdaa01e4fd0a858c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d40a24d628d76be52ee64513e97c10cb1942d936da2ee27bdaa01e4fd0a858c","first_computed_at":"2026-05-18T00:00:23.701661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:23.701661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OxQ+lQElJTqlXh9lnFOkYr3WHeI+Dk9s98MunEXIqGTWt98Na6G+++hUPepCI5ulmapAi269LaPIQDsLjlbhBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:23.702247Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.07704","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3be8187a6744a0bb5825a71a9efd91bb6191e8bbe41c4f1521a25ec059dfd17","sha256:47b32a0cde99f13a0b2a179aec57a9a02139f885a9fd19ff44848a508fbac14d"],"state_sha256":"ef2fb0fe14a4faffc32d0ecc1fa203926e59f4ee79ba3f73c0a3898c72a12d60"}