{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6IOIRY2435SSNFRXTHNA6VUCEL","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":"8ce27d64074b6eeba71cd6db7b897db47f24a9fbc52f35939f4c1331b5a4741e","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-01-23T21:15:16Z","title_canon_sha256":"34568b3597fe48de43bd014b44b68768a7b076601e28edf842db7be4bfb32147"},"schema_version":"1.0","source":{"id":"1401.6189","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6189","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6189v1","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6189","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"pith_short_12","alias_value":"6IOIRY2435SS","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6IOIRY2435SSNFRX","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6IOIRY24","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:efa166496802022bf313cde7dd7d7dc48b2ae5184748f84c1b215940ed4d024f","target":"graph","created_at":"2026-05-18T03:01:12Z","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":"We describe a construction of explicit affine extractors over large finite fields with exponentially small error and linear output length. Our construction relies on a deep theorem of Deligne giving tight estimates for exponential sums over smooth varieties in high dimensions.","authors_text":"Ethan Leeman, Jean Bourgain, Zeev Dvir","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-01-23T21:15:16Z","title":"Affine extractors over large fields with exponential error"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6189","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":"sha256:89de5c07757675779c144739f2a19aa50aca22731ac932c509676f50d3d8fc92","target":"record","created_at":"2026-05-18T03:01:12Z","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":"8ce27d64074b6eeba71cd6db7b897db47f24a9fbc52f35939f4c1331b5a4741e","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-01-23T21:15:16Z","title_canon_sha256":"34568b3597fe48de43bd014b44b68768a7b076601e28edf842db7be4bfb32147"},"schema_version":"1.0","source":{"id":"1401.6189","kind":"arxiv","version":1}},"canonical_sha256":"f21c88e35cdf6526963799da0f568222c6df4321a952cbe51fe4158faf0352aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f21c88e35cdf6526963799da0f568222c6df4321a952cbe51fe4158faf0352aa","first_computed_at":"2026-05-18T03:01:12.948992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:12.948992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T4DC485BcVtXd+KlTkXoGHSN4o6YaabGMDwl5d5CXScUAoKJZhFli9CEbegzp/oU4+/GEZ8D6sMxK3yr7tfwCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:12.949686Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.6189","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89de5c07757675779c144739f2a19aa50aca22731ac932c509676f50d3d8fc92","sha256:efa166496802022bf313cde7dd7d7dc48b2ae5184748f84c1b215940ed4d024f"],"state_sha256":"0a030dbc4ba563e658932e388a9b10e579683050c604e4f34a6db15b1f2aea2e"}