{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IZ4QROE65MQVLPRXVDLK7YLQPD","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":"33852f85727b07a14d6dbd32bc1091f311b4975ea6b689686a0311dd07f01d79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-20T18:20:26Z","title_canon_sha256":"c03c49e8dda411a2231977871275e20016904a3173fb5537e525d00fde4e07f6"},"schema_version":"1.0","source":{"id":"1612.06791","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06791","created_at":"2026-05-18T00:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06791v1","created_at":"2026-05-18T00:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06791","created_at":"2026-05-18T00:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"IZ4QROE65MQV","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IZ4QROE65MQVLPRX","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IZ4QROE6","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:fbe8688dcab32fb3591342bacdaa39776b2c1552254ad3a821dd59e12d4af7f5","target":"graph","created_at":"2026-05-18T00:54:21Z","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 discuss completeness, minimality, and basisness, in $L^2[0, \\pi]$ and $L^p[0, \\pi]$, $p \\neq 2$, of dilated systems $u_n(x) = S(nx)$, $n \\in \\mathbb{N}$, where $S$ is a trigonometric polynomial\n  $S(x) = \\sum_{k = 0}^m a_k \\sin(kx), \\quad a_0 a_m \\neq 0.$\n  We will present some results and mention a few unsolved questions.","authors_text":"Boris Mityagin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-20T18:20:26Z","title":"Systems of Dilated Functions: completeness, minimality, basisness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06791","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":"sha256:325b23c0bb9b00632c9a27893622b43ef7c8a61214af6915d838cc40d6be37a6","target":"record","created_at":"2026-05-18T00:54:21Z","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":"33852f85727b07a14d6dbd32bc1091f311b4975ea6b689686a0311dd07f01d79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-20T18:20:26Z","title_canon_sha256":"c03c49e8dda411a2231977871275e20016904a3173fb5537e525d00fde4e07f6"},"schema_version":"1.0","source":{"id":"1612.06791","kind":"arxiv","version":1}},"canonical_sha256":"467908b89eeb2155be37a8d6afe17078e3e67dec5fa6a376fd509acd275bf19c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"467908b89eeb2155be37a8d6afe17078e3e67dec5fa6a376fd509acd275bf19c","first_computed_at":"2026-05-18T00:54:21.486132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:21.486132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FfVa40rkP4MoPHZn+WP8cGHiGc5fV2lF8cwEXA/EI/8Tebc+0TQhCphPieRpW636KUf8XtgXtdBeTVpaeZ7cBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:21.486484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06791","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:325b23c0bb9b00632c9a27893622b43ef7c8a61214af6915d838cc40d6be37a6","sha256:fbe8688dcab32fb3591342bacdaa39776b2c1552254ad3a821dd59e12d4af7f5"],"state_sha256":"6039a215016b20ba44df2118f15f99cfd1a302c0d489bf76d64635489bf8b17f"}