{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:N2RDLAOCWLXJWG6R25CFSQSOGN","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":"b644732a01aebc342263e391cffccab6f8bd927bd9be916ac2eed7da0027e201","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-19T14:39:49Z","title_canon_sha256":"7ef07f2b505ea20a530b5683dbabf08aa803b2ad9dbe16cd506ab1d493c43f79"},"schema_version":"1.0","source":{"id":"1302.4622","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4622","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4622v1","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4622","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"pith_short_12","alias_value":"N2RDLAOCWLXJ","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"N2RDLAOCWLXJWG6R","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"N2RDLAOC","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:cf7019f641aa635a0a15d8ac44353c3e6ed82469d661e9aa8ff798c2e9624655","target":"graph","created_at":"2026-05-18T03:33:12Z","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 are interested in the following problem. Let $p$ be a prime number, $S\\subset \\F_p$ and $\\cP\\subset \\{P\\in\\F_p [X]:\\deg P\\le d\\}$. What is the largest integer $k$ such that for all subsets $\\cA, \\cB$ of $\\F_p$ satisfying $\\cA\\cap\\cB =\\emptyset$ and $|\\cA\\cup\\cB |=k$, there exists $P\\in\\cP$ such that $P(x)\\in S$ if $x\\in\\cA$ and $P(x)\\not\\in S$ if $x\\in\\cB$? This problem corresponds to the study of the complexity of some families of pseudo-random subsets. First we recall this complexity definition and the context of pseudo-random subsets. Then we state the different results we ","authors_text":"C\\'ecile Dartyge (IECL), Elie Mosaki (ICJ), Ramachandran Balasubramanian (CIT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-19T14:39:49Z","title":"Sur la complexit\\'e de familles d'ensembles pseudo-al\\'eatoires"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4622","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":"sha256:85c2c6706037010c76372c99cce4b962a5c4eaaec03fac9d606339a59f294849","target":"record","created_at":"2026-05-18T03:33:12Z","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":"b644732a01aebc342263e391cffccab6f8bd927bd9be916ac2eed7da0027e201","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-19T14:39:49Z","title_canon_sha256":"7ef07f2b505ea20a530b5683dbabf08aa803b2ad9dbe16cd506ab1d493c43f79"},"schema_version":"1.0","source":{"id":"1302.4622","kind":"arxiv","version":1}},"canonical_sha256":"6ea23581c2b2ee9b1bd1d74459424e3372f39733467ffef3905e5283e808b6ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ea23581c2b2ee9b1bd1d74459424e3372f39733467ffef3905e5283e808b6ad","first_computed_at":"2026-05-18T03:33:12.690987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:12.690987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gZyKWex6o01Ojv7OWtN2S1ZEKMQaJQDlXh3yIWHbSoRDScWigmn3NrAEZPQULOlcm98duBHmJIVTnsok+GNbDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:12.691896Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4622","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85c2c6706037010c76372c99cce4b962a5c4eaaec03fac9d606339a59f294849","sha256:cf7019f641aa635a0a15d8ac44353c3e6ed82469d661e9aa8ff798c2e9624655"],"state_sha256":"84cfe38823cd9ff8de0ef996a75a3b8f59da1cbca8136c985ffb39649bc3eb9f"}