{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BIZCK5X3WUBYS3R47UQLBMP2Z7","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":"ce8c82a7694216fe7b36662c969c640bc652d7e9e2bda9e680da9652fd00b52a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2018-08-15T04:20:22Z","title_canon_sha256":"61a2dd606adbc97304dc166f9ef140f4ea7baa1bfc2b96b681a3bd507dd563cf"},"schema_version":"1.0","source":{"id":"1808.04965","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.04965","created_at":"2026-05-17T23:43:23Z"},{"alias_kind":"arxiv_version","alias_value":"1808.04965v2","created_at":"2026-05-17T23:43:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.04965","created_at":"2026-05-17T23:43:23Z"},{"alias_kind":"pith_short_12","alias_value":"BIZCK5X3WUBY","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BIZCK5X3WUBYS3R4","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BIZCK5X3","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:ae62364156eb70619ed2bb09d8a9cae0934c62587c602e00cc415b49b61f0310","target":"graph","created_at":"2026-05-17T23:43:23Z","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":"The Bogolyubov-Ruzsa lemma, in particular the quantitative bounds obtained by Sanders, plays a central role in obtaining effective bounds for the inverse $U^3$ theorem for the Gowers norms. Recently, Gowers and Mili\\'cevi\\'c applied a bilinear Bogolyubov-Ruzsa lemma as part of a proof of the inverse $U^4$ theorem with effective bounds. The goal of this note is to obtain quantitative bounds for the bilinear Bogolyubov-Ruzsa lemma which are similar to those obtained by Sanders for the Bogolyubov-Ruzsa lemma.\n  We show that if a set $A \\subset \\mathbb{F}_p^n \\times \\mathbb{F}_p^n$ has density $\\a","authors_text":"Kaave Hosseini, Shachar Lovett","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2018-08-15T04:20:22Z","title":"A bilinear Bogolyubov-Ruzsa lemma with poly-logarithmic bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04965","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:a8bf5de680fbfaa671d2332468de9d9483d3b34d3aa481894d5cca52873a6357","target":"record","created_at":"2026-05-17T23:43:23Z","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":"ce8c82a7694216fe7b36662c969c640bc652d7e9e2bda9e680da9652fd00b52a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2018-08-15T04:20:22Z","title_canon_sha256":"61a2dd606adbc97304dc166f9ef140f4ea7baa1bfc2b96b681a3bd507dd563cf"},"schema_version":"1.0","source":{"id":"1808.04965","kind":"arxiv","version":2}},"canonical_sha256":"0a322576fbb503896e3cfd20b0b1facfc9fc0696bb301a30dec42b85f12d8e06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a322576fbb503896e3cfd20b0b1facfc9fc0696bb301a30dec42b85f12d8e06","first_computed_at":"2026-05-17T23:43:23.720839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:23.720839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J/AyvwH33WgqCKQ+0c09V6v4Pc2LtUqC2/D/LHsMM51dIDTLdbanUPsYMsaFbw5jKUint2oN2wFHNKF2O4i7Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:23.721556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.04965","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8bf5de680fbfaa671d2332468de9d9483d3b34d3aa481894d5cca52873a6357","sha256:ae62364156eb70619ed2bb09d8a9cae0934c62587c602e00cc415b49b61f0310"],"state_sha256":"0ecf8dc66a6f125d713e674c40df7804e5131ca5c2e274ae4eb31b5236e84230"}