{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ODRRVNRERZ344BXM47VMMAMOC4","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":"5b28260ae80653ff8de1f38576d27dd269e1b3611e6d7e4eda009eee74a352e7","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-02-27T19:24:32Z","title_canon_sha256":"cef221a0dea21f424ff8bdd67d42c7f99b49b8d2bbe99dc547c28967cd824cd4"},"schema_version":"1.0","source":{"id":"1102.5538","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5538","created_at":"2026-05-18T04:13:05Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5538v4","created_at":"2026-05-18T04:13:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5538","created_at":"2026-05-18T04:13:05Z"},{"alias_kind":"pith_short_12","alias_value":"ODRRVNRERZ34","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"ODRRVNRERZ344BXM","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"ODRRVNRE","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:c80c23ff84a0f4802c8c0468f4c1682a1e02a740dbf4cfd083917dac3ed84924","target":"graph","created_at":"2026-05-18T04:13:05Z","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 probabilistic bit-probe schemes for the membership problem. Given a set A of at most n elements from the universe of size m we organize such a structure that queries of type \"Is x in A?\" can be answered very quickly. H.Buhrman, P.B.Miltersen, J.Radhakrishnan, and S.Venkatesh proposed a bit-probe scheme based on expanders. Their scheme needs space of $O(n\\log m)$ bits, and requires to read only one randomly chosen bit from the memory to answer a query. The answer is correct with high probability with two-sided errors. In this paper we show that for the same problem there exists a bit-p","authors_text":"Andrei Romashchenko","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-02-27T19:24:32Z","title":"Pseudo-random graphs and bit probe schemes with one-sided error"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5538","kind":"arxiv","version":4},"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":"sha256:034565e884d338988d23d3c69e017c82d3ef3d93421bc007e01c96803b18b26d","target":"record","created_at":"2026-05-18T04:13:05Z","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":"5b28260ae80653ff8de1f38576d27dd269e1b3611e6d7e4eda009eee74a352e7","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-02-27T19:24:32Z","title_canon_sha256":"cef221a0dea21f424ff8bdd67d42c7f99b49b8d2bbe99dc547c28967cd824cd4"},"schema_version":"1.0","source":{"id":"1102.5538","kind":"arxiv","version":4}},"canonical_sha256":"70e31ab6248e77ce06ece7eac6018e173bd4dbafd36ab67653d0b36e8c83c1eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70e31ab6248e77ce06ece7eac6018e173bd4dbafd36ab67653d0b36e8c83c1eb","first_computed_at":"2026-05-18T04:13:05.585737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:05.585737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t0RhAe52jnnzAbLke/Y2EOsRGD4kMnLtOhSwXKtDz65/Nf4X2osiOpaeSwA/05cW1JpOixUgnGx+pKolZ3NtBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:05.586462Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.5538","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:034565e884d338988d23d3c69e017c82d3ef3d93421bc007e01c96803b18b26d","sha256:c80c23ff84a0f4802c8c0468f4c1682a1e02a740dbf4cfd083917dac3ed84924"],"state_sha256":"ff8a6ce4f03f8b0c1057b1f4ec74527785c66dd6ff39e0cd4af0606fdd5b6c1b"}