{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:334NILXYBEA4XSOFAOZZXFTN3Q","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":"06c3825494b25dfee0625d7caec9500cdf3353f0c4c0c45bd6d95b4b9000b805","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-13T03:46:16Z","title_canon_sha256":"ee72126f8f550d14723ad7b88f16378fcd89602e2b859112a148f98e029cc799"},"schema_version":"1.0","source":{"id":"1405.3027","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3027","created_at":"2026-05-18T02:46:32Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3027v2","created_at":"2026-05-18T02:46:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3027","created_at":"2026-05-18T02:46:32Z"},{"alias_kind":"pith_short_12","alias_value":"334NILXYBEA4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"334NILXYBEA4XSOF","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"334NILXY","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:4079a967939aaf3f7b93a5f9ccca48d08aebbe83037a40650738bafaacfed2dc","target":"graph","created_at":"2026-05-18T02:46:32Z","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 determine upper bounds on the number of rational points of an affine or projective algebraic set defined over an extension of a finite field by a system of polynomial equations, including the case where the algebraic set is not defined over the finite field by itself. A special attention is given to irreducible but not absolutely irreducible algebraic sets, which satisfy better bounds. We study the case of complete intersections, for which we give a decomposition, coarser than the decomposition in irreducible components, but more directly related to the polynomials defining the algebraic se","authors_text":"Gilles Lachaud, Robert Rolland","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-13T03:46:16Z","title":"On the Number of Points of Algebraic Sets over Finite Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3027","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":"sha256:6d9fbc02e6bdd4fadf235357881fabc004547bc41562c4db01a41de8606d7ad9","target":"record","created_at":"2026-05-18T02:46:32Z","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":"06c3825494b25dfee0625d7caec9500cdf3353f0c4c0c45bd6d95b4b9000b805","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-13T03:46:16Z","title_canon_sha256":"ee72126f8f550d14723ad7b88f16378fcd89602e2b859112a148f98e029cc799"},"schema_version":"1.0","source":{"id":"1405.3027","kind":"arxiv","version":2}},"canonical_sha256":"def8d42ef80901cbc9c503b39b966ddc273425a53fe01b0117617c1fc6becc0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"def8d42ef80901cbc9c503b39b966ddc273425a53fe01b0117617c1fc6becc0d","first_computed_at":"2026-05-18T02:46:32.508048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:32.508048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DkD2qDcOouOsddb44Y3FhT1//5NC0DYD6BBaIieoL0akCcAd53m8QaA6UYbZzxQnv0fLmPMI9Tvfp5JDyV6KCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:32.508492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.3027","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d9fbc02e6bdd4fadf235357881fabc004547bc41562c4db01a41de8606d7ad9","sha256:4079a967939aaf3f7b93a5f9ccca48d08aebbe83037a40650738bafaacfed2dc"],"state_sha256":"fba0e68b600d037a604536ec764b08099a65e87587efc86998f15c9a080e341b"}