{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Y5ESV7QBUSIRPVGYSNF66G3YGI","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":"43779ac320d8969591e0a1be72d134d453e36e7ecea31c66815ab53fc5e55d3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-31T20:56:48Z","title_canon_sha256":"c5e3f47f5ab178f03dc727f45399a5385e7d5be81b11182a137b88d452982ba6"},"schema_version":"1.0","source":{"id":"1709.00080","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.00080","created_at":"2026-05-18T00:33:58Z"},{"alias_kind":"arxiv_version","alias_value":"1709.00080v3","created_at":"2026-05-18T00:33:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00080","created_at":"2026-05-18T00:33:58Z"},{"alias_kind":"pith_short_12","alias_value":"Y5ESV7QBUSIR","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"Y5ESV7QBUSIRPVGY","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"Y5ESV7QB","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:e9c31050ac3608bcde9b51b7ee028a301255d6da114562164cbc1dddd8788d13","target":"graph","created_at":"2026-05-18T00:33:58Z","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 prove that, under certain conditions on the function pair $\\varphi_1$ and $\\varphi_2$, bilinear average $p^{-1}\\sum_{y\\in \\mathbb{F}_p}f_1(x+\\varphi_1(y)) f_2(x+\\varphi_2(y))$ along curve $(\\varphi_1, \\varphi_2)$ satisfies certain decay estimate. As a consequence, Roth type theorems hold in the setting of finite fields. In particular, if $\\varphi_1,\\varphi_2\\in \\mathbb{F}_p[X]$ with $\\varphi_1(0)=\\varphi_2(0)=0$ are linearly independent polynomials, then for any $A\\subset \\mathbb{F}_p, |A|=\\delta p$ with $\\delta>c p^{-\\frac{1}{12}}$, there are $\\gtrsim \\delta^3p^2$ triplets $x,x+\\varphi_1(y","authors_text":"Dong Dong, Will Sawin, Xiaochun Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-31T20:56:48Z","title":"Improved estimates for polynomial Roth type theorems in finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00080","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":"sha256:6798b3d7eafe53dad9e431a6131630b6a6f1f50982981f02f603d07c19edf2b1","target":"record","created_at":"2026-05-18T00:33:58Z","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":"43779ac320d8969591e0a1be72d134d453e36e7ecea31c66815ab53fc5e55d3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-31T20:56:48Z","title_canon_sha256":"c5e3f47f5ab178f03dc727f45399a5385e7d5be81b11182a137b88d452982ba6"},"schema_version":"1.0","source":{"id":"1709.00080","kind":"arxiv","version":3}},"canonical_sha256":"c7492afe01a49117d4d8934bef1b783211cf2e0d9177b3a17ebc66566dd93c1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7492afe01a49117d4d8934bef1b783211cf2e0d9177b3a17ebc66566dd93c1e","first_computed_at":"2026-05-18T00:33:58.525992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:58.525992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iUS4yOpPwXBncu7NxSzHTWIw97f3ve7OtH7LIlfV4G00yucC5IrFEA4mvqKXKcdsJjmqSWX22ggSIuWCnkJiDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:58.526625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.00080","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6798b3d7eafe53dad9e431a6131630b6a6f1f50982981f02f603d07c19edf2b1","sha256:e9c31050ac3608bcde9b51b7ee028a301255d6da114562164cbc1dddd8788d13"],"state_sha256":"5e0b99f78b54889ce8f26a7f8908479659c21b030be1dfc3d117187d5eeea743"}