{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MSXGCFKZ73RE5KASUKUNWYYLFG","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":"6c5009f760e2e1f1d88b80076082c36a1f7e123cbfc1dd2c596f308554d02054","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-07-15T14:50:59Z","title_canon_sha256":"556b8c11cc19c40c9112fb2323350e13b804f1a798de4cab3603aa87b9da2454"},"schema_version":"1.0","source":{"id":"1307.3975","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3975","created_at":"2026-05-18T03:18:27Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3975v1","created_at":"2026-05-18T03:18:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3975","created_at":"2026-05-18T03:18:27Z"},{"alias_kind":"pith_short_12","alias_value":"MSXGCFKZ73RE","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MSXGCFKZ73RE5KAS","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MSXGCFKZ","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:cc764a69aaa5b6e9f3c43fc5f458efd0c3a3feada97b17731f3e941cd53e90de","target":"graph","created_at":"2026-05-18T03:18:27Z","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":"A low-degree test is a collection of simple, local rules for checking the proximity of an arbitrary function to a low-degree polynomial. Each rule depends on the function's values at a small number of places. If a function satisfies many rules then it is close to a low-degree polynomial. Low-degree tests play an important role in the development of probabilistically checkable proofs.\n  In this paper we present two improvements to the efficiency of low-degree tests. Our first improvement concerns the smallest field size over which a low-degree test can work. We show how to test that a function ","authors_text":"Katalin Friedl, Madhu Sudan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-07-15T14:50:59Z","title":"Some Improvements to Total Degree Tests"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3975","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":"sha256:3a76bd56e6557d1d5364a7bd41c2463d1eae70fd4fd337bffc35ea8f4dad2bb9","target":"record","created_at":"2026-05-18T03:18:27Z","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":"6c5009f760e2e1f1d88b80076082c36a1f7e123cbfc1dd2c596f308554d02054","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-07-15T14:50:59Z","title_canon_sha256":"556b8c11cc19c40c9112fb2323350e13b804f1a798de4cab3603aa87b9da2454"},"schema_version":"1.0","source":{"id":"1307.3975","kind":"arxiv","version":1}},"canonical_sha256":"64ae611559fee24ea812a2a8db630b29986e42ce5f580302279e41a94f18d729","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64ae611559fee24ea812a2a8db630b29986e42ce5f580302279e41a94f18d729","first_computed_at":"2026-05-18T03:18:27.283290Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:27.283290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8KfnNk0B8AYBXa3Yl49ImOqz5k2aBD/ll1cEfWi19Skb1tJOePTU9fgpmkYfinRq6OlyqmOIj63UMteVnb64CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:27.283951Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3975","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a76bd56e6557d1d5364a7bd41c2463d1eae70fd4fd337bffc35ea8f4dad2bb9","sha256:cc764a69aaa5b6e9f3c43fc5f458efd0c3a3feada97b17731f3e941cd53e90de"],"state_sha256":"a37f0103ac52240be47f29eb092230ad3bae01f6c40f7a2620ebde2db0a89812"}