{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:T3SDPUKE7CYRB75GT7DFCPHC6Z","short_pith_number":"pith:T3SDPUKE","schema_version":"1.0","canonical_sha256":"9ee437d144f8b110ffa69fc6513ce2f67ff4960f32f210b4e6d370bcd771edfc","source":{"kind":"arxiv","id":"1606.01230","version":6},"attestation_state":"computed","paper":{"title":"A tight bound for Green's arithmetic triangle removal lemma in vector spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jacob Fox, L\\'aszl\\'o Mikl\\'os Lov\\'asz","submitted_at":"2016-06-03T19:45:25Z","abstract_excerpt":"Let $p$ be a fixed prime. A triangle in $\\mathbb{F}_p^n$ is an ordered triple $(x,y,z)$ of points satisfying $x+y+z=0$. Let $N=p^n=|\\mathbb{F}_p^n|$. Green proved an arithmetic triangle removal lemma which says that for every $\\epsilon>0$ and prime $p$, there is a $\\delta>0$ such that if $X,Y,Z \\subset \\mathbb{F}_p^n$ and the number of triangles in $X \\times Y \\times Z$ is at most $\\delta N^2$, then we can delete $\\epsilon N$ elements from $X$, $Y$, and $Z$ and remove all triangles. Green posed the problem of improving the quantitative bounds on the arithmetic triangle removal lemma, and, in p"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.01230","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-03T19:45:25Z","cross_cats_sorted":[],"title_canon_sha256":"d10591cb4b4d166a9e1bf09e6e3e4fbaf1925e97a5ee972eed5402751d3f3b7d","abstract_canon_sha256":"079202c2ed6cb03c1cd9f08301c285bd3f217651a281884b01730f6a36bcc7d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:44.273665Z","signature_b64":"ZuSuku19RLT3MfL95h1+2mZ6sMAADmwKudy1OO2wz1qtEtsF46GaE1jks0y1mr1BNITgI20/h9y3l64DwN/UBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ee437d144f8b110ffa69fc6513ce2f67ff4960f32f210b4e6d370bcd771edfc","last_reissued_at":"2026-05-18T00:35:44.273249Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:44.273249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A tight bound for Green's arithmetic triangle removal lemma in vector spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jacob Fox, L\\'aszl\\'o Mikl\\'os Lov\\'asz","submitted_at":"2016-06-03T19:45:25Z","abstract_excerpt":"Let $p$ be a fixed prime. A triangle in $\\mathbb{F}_p^n$ is an ordered triple $(x,y,z)$ of points satisfying $x+y+z=0$. Let $N=p^n=|\\mathbb{F}_p^n|$. Green proved an arithmetic triangle removal lemma which says that for every $\\epsilon>0$ and prime $p$, there is a $\\delta>0$ such that if $X,Y,Z \\subset \\mathbb{F}_p^n$ and the number of triangles in $X \\times Y \\times Z$ is at most $\\delta N^2$, then we can delete $\\epsilon N$ elements from $X$, $Y$, and $Z$ and remove all triangles. Green posed the problem of improving the quantitative bounds on the arithmetic triangle removal lemma, and, in p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01230","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.01230","created_at":"2026-05-18T00:35:44.273311+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.01230v6","created_at":"2026-05-18T00:35:44.273311+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01230","created_at":"2026-05-18T00:35:44.273311+00:00"},{"alias_kind":"pith_short_12","alias_value":"T3SDPUKE7CYR","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"T3SDPUKE7CYRB75G","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"T3SDPUKE","created_at":"2026-05-18T12:30:44.179134+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T3SDPUKE7CYRB75GT7DFCPHC6Z","json":"https://pith.science/pith/T3SDPUKE7CYRB75GT7DFCPHC6Z.json","graph_json":"https://pith.science/api/pith-number/T3SDPUKE7CYRB75GT7DFCPHC6Z/graph.json","events_json":"https://pith.science/api/pith-number/T3SDPUKE7CYRB75GT7DFCPHC6Z/events.json","paper":"https://pith.science/paper/T3SDPUKE"},"agent_actions":{"view_html":"https://pith.science/pith/T3SDPUKE7CYRB75GT7DFCPHC6Z","download_json":"https://pith.science/pith/T3SDPUKE7CYRB75GT7DFCPHC6Z.json","view_paper":"https://pith.science/paper/T3SDPUKE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.01230&json=true","fetch_graph":"https://pith.science/api/pith-number/T3SDPUKE7CYRB75GT7DFCPHC6Z/graph.json","fetch_events":"https://pith.science/api/pith-number/T3SDPUKE7CYRB75GT7DFCPHC6Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T3SDPUKE7CYRB75GT7DFCPHC6Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T3SDPUKE7CYRB75GT7DFCPHC6Z/action/storage_attestation","attest_author":"https://pith.science/pith/T3SDPUKE7CYRB75GT7DFCPHC6Z/action/author_attestation","sign_citation":"https://pith.science/pith/T3SDPUKE7CYRB75GT7DFCPHC6Z/action/citation_signature","submit_replication":"https://pith.science/pith/T3SDPUKE7CYRB75GT7DFCPHC6Z/action/replication_record"}},"created_at":"2026-05-18T00:35:44.273311+00:00","updated_at":"2026-05-18T00:35:44.273311+00:00"}