{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:I3GHGHLSPSFBBMORLLLBLC5IR2","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":"b30d6ba85e8d9e6892cc18714f91b47a9d9401aae98d48af8c4792b300fbeb08","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-09-22T20:07:08Z","title_canon_sha256":"f89a8d1042c30a6ecb04031ae8ac3d21d6094da2c712114e4d64740e603d3b79"},"schema_version":"1.0","source":{"id":"2009.10789","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.10789","created_at":"2026-07-05T02:34:09Z"},{"alias_kind":"arxiv_version","alias_value":"2009.10789v2","created_at":"2026-07-05T02:34:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.10789","created_at":"2026-07-05T02:34:09Z"},{"alias_kind":"pith_short_12","alias_value":"I3GHGHLSPSFB","created_at":"2026-07-05T02:34:09Z"},{"alias_kind":"pith_short_16","alias_value":"I3GHGHLSPSFBBMOR","created_at":"2026-07-05T02:34:09Z"},{"alias_kind":"pith_short_8","alias_value":"I3GHGHLS","created_at":"2026-07-05T02:34:09Z"}],"graph_snapshots":[{"event_id":"sha256:a21976c51d854eea5882950df2a831c77ef8822a20f9487c2d282143126a62cb","target":"graph","created_at":"2026-07-05T02:34:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2009.10789/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a sampling discretization theorem for the square norm of functions from a finite dimensional subspace satisfying Nikol'skii's inequality with an upper bound on the number of sampling points of the order of the dimension of the subspace","authors_text":"Irina Limonova, Vladimir Temlyakov","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-09-22T20:07:08Z","title":"On sampling discretization in $L_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.10789","kind":"arxiv","version":2},"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":"sha256:81eb8ea891872e744772a0e57290c018a6ee27f83eb7948dc359ca8e7b97f10a","target":"record","created_at":"2026-07-05T02:34:09Z","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":"b30d6ba85e8d9e6892cc18714f91b47a9d9401aae98d48af8c4792b300fbeb08","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-09-22T20:07:08Z","title_canon_sha256":"f89a8d1042c30a6ecb04031ae8ac3d21d6094da2c712114e4d64740e603d3b79"},"schema_version":"1.0","source":{"id":"2009.10789","kind":"arxiv","version":2}},"canonical_sha256":"46cc731d727c8a10b1d15ad6158ba88e99064d584b8faa07f4f628552b284f72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46cc731d727c8a10b1d15ad6158ba88e99064d584b8faa07f4f628552b284f72","first_computed_at":"2026-07-05T02:34:09.288087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:34:09.288087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RwgG+/Qv7V9DCNhJc0JPpLrOtowZph8d8V8S2hZDq0PRQ76LgNttY2Nq0H3BnfP1pOiv2jBASM1Nl/Sxi+Q9Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:34:09.288564Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.10789","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81eb8ea891872e744772a0e57290c018a6ee27f83eb7948dc359ca8e7b97f10a","sha256:a21976c51d854eea5882950df2a831c77ef8822a20f9487c2d282143126a62cb"],"state_sha256":"4f5a235e223823895b4d22c7385e9fceaadab74d3a1ba4d97ec3846aab43d8e9"}