{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:M7QTWHW5YXT2QNJ7SIO7IL25L3","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":"499df042d8d7d34b34195e0695fa853bbc2550b16717fc39b073eeda7c3ccbb3","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-01T11:13:21Z","title_canon_sha256":"42089704b9bd4311641accf2d32f7192fabd83dc1bc2e631528649de45770175"},"schema_version":"1.0","source":{"id":"1203.0146","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.0146","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"arxiv_version","alias_value":"1203.0146v1","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0146","created_at":"2026-05-18T00:42:08Z"},{"alias_kind":"pith_short_12","alias_value":"M7QTWHW5YXT2","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M7QTWHW5YXT2QNJ7","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M7QTWHW5","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:d52238e41f123406de85544d964b2c59e54957db39716b8d76b3359c755ceae2","target":"graph","created_at":"2026-05-18T00:42:08Z","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 study the random sampling of band-limited functions of several variables. If a bandlimited function with bandwidth one has its essential support on a cube of volume $R^d$, then $\\cO (R^d \\log R^d)$ random samples suffice to approximate the function up to a given error with high probability.","authors_text":"Karlheinz Gr\\\"ochenig, Richard F. Bass","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-01T11:13:21Z","title":"Relevant Sampling of Band-limited Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0146","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:e86ba4fadba07a3c2285889a084bf86e9a424feb5a8c4f05033a80b6ed0a3f9e","target":"record","created_at":"2026-05-18T00:42:08Z","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":"499df042d8d7d34b34195e0695fa853bbc2550b16717fc39b073eeda7c3ccbb3","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-01T11:13:21Z","title_canon_sha256":"42089704b9bd4311641accf2d32f7192fabd83dc1bc2e631528649de45770175"},"schema_version":"1.0","source":{"id":"1203.0146","kind":"arxiv","version":1}},"canonical_sha256":"67e13b1eddc5e7a8353f921df42f5d5ed6e43ea8d87618264ab0b91cf0d43859","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67e13b1eddc5e7a8353f921df42f5d5ed6e43ea8d87618264ab0b91cf0d43859","first_computed_at":"2026-05-18T00:42:08.127644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:08.127644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"90BAt0Tq/7iAQWJmT6rD2RVEeEmuA2shuPOboGXWFhUHH8RH5u0IoYA79FdWkjEBLeetHM6mWQROPj1U90gHBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:08.128060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.0146","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e86ba4fadba07a3c2285889a084bf86e9a424feb5a8c4f05033a80b6ed0a3f9e","sha256:d52238e41f123406de85544d964b2c59e54957db39716b8d76b3359c755ceae2"],"state_sha256":"7eeb6915d6aee71fbd052f3cd7079339297c2ed6bab909636db9007b2cf7af17"}