{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:D5NL3SHRRYWORXTENCB6XYXS3S","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":"c0931a46c152654ebdd86e842502a0f88086ace0fd3ec89049bf6e4946e535f9","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2004-12-02T21:30:06Z","title_canon_sha256":"0b5bb0efa346bf10cf0b33a5ff8c907111c514bca42abdeb90dd70ffd67bbd57"},"schema_version":"1.0","source":{"id":"math/0412063","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0412063","created_at":"2026-05-18T04:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"math/0412063v3","created_at":"2026-05-18T04:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0412063","created_at":"2026-05-18T04:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"D5NL3SHRRYWO","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"D5NL3SHRRYWORXTE","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"D5NL3SHR","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:5401139823fcaffd8975cd84df4870aa612ce1cb2f0fdcd856487315a11b2954","target":"graph","created_at":"2026-05-18T04:35:55Z","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 consider incomplete exponential sums in several variables of the form S(f,n,m) = \\frac{1}{2^n} \\sum_{x_1 \\in \\{-1,1\\}} ... \\sum_{x_n \\in \\{-1,1\\}} x_1 ... x_n e^{2\\pi i f(x)/p}, where m>1 is odd and f is a polynomial of degree d with coefficients in Z/mZ. We investigate the conjecture, originating in a problem in computational complexity, that for each fixed d and m the maximum norm of S(f,n,m) converges exponentially fast to 0 as n grows to infinity. The conjecture is known to hold in the case when m=3 and d=2, but existing methods for studying incomplete exponential sums appear to be insu","authors_text":"Amitabha Roy, Eduardo Duenez, Howard Straubing, Steven J. Miller","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2004-12-02T21:30:06Z","title":"Incomplete Quadratic Exponential Sums in Several Variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412063","kind":"arxiv","version":3},"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":"sha256:48693b1da067a24d250c1aceeb51198402b96303b4f5bb5487db8a3df35ab6a9","target":"record","created_at":"2026-05-18T04:35:55Z","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":"c0931a46c152654ebdd86e842502a0f88086ace0fd3ec89049bf6e4946e535f9","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2004-12-02T21:30:06Z","title_canon_sha256":"0b5bb0efa346bf10cf0b33a5ff8c907111c514bca42abdeb90dd70ffd67bbd57"},"schema_version":"1.0","source":{"id":"math/0412063","kind":"arxiv","version":3}},"canonical_sha256":"1f5abdc8f18e2ce8de646883ebe2f2dca616b431753f1dd33d2ab0e84ba8c5ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f5abdc8f18e2ce8de646883ebe2f2dca616b431753f1dd33d2ab0e84ba8c5ce","first_computed_at":"2026-05-18T04:35:55.537357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:55.537357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pJ7JQc38dUIlsxgvq5w8szjJMNn+kjSn2h7i7t+6kkdtwsnqx8I6M1pp7ha6apvWAa64CTw0Vpog6hgpVPQZCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:55.537919Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0412063","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48693b1da067a24d250c1aceeb51198402b96303b4f5bb5487db8a3df35ab6a9","sha256:5401139823fcaffd8975cd84df4870aa612ce1cb2f0fdcd856487315a11b2954"],"state_sha256":"ca1aee6fb590018d4e3535f8b2df19c0e949148c314847e33af4e832a06b9f89"}