{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:RJBHKHQOU2JZWHPOKRCBDPB6HS","short_pith_number":"pith:RJBHKHQO","schema_version":"1.0","canonical_sha256":"8a42751e0ea6939b1dee544411bc3e3cbac06ac81f00dfbe4df4cb8a0f47d15a","source":{"kind":"arxiv","id":"1812.00654","version":1},"attestation_state":"computed","paper":{"title":"Constructions for the Elekes-Szab\\'o and Elekes-R\\'onyai problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Audie Warren, Frank de Zeeuw, Mehdi Makhul, Oliver Roche-Newton","submitted_at":"2018-12-03T10:40:54Z","abstract_excerpt":"We give a construction of a non-degenerate polynomial $F\\in \\mathbb R[x,y,z]$ and a set $A$ of cardinality $n$ such that $\\left|Z(F)\\cap (A \\times A \\times A) \\right| \\gg n^{\\frac{3}{2}}$, thus providing a new lower bound construction for the Elekes--Szab\\'o problem. We also give a related construction for the Elekes--R\\'onyai problem restricted to a subgraph. This consists of a polynomial $f\\in \\mathbb R[x,y]$ that is not additive or multiplicative, a set $A$ of size $n$, and a subset $P\\subset A\\times A$ of size $|P|\\gg n^{3/2}$ on which $f$ takes only $n$ distinct values."},"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":"1812.00654","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-03T10:40:54Z","cross_cats_sorted":[],"title_canon_sha256":"86226696bbb1ecb8e51508d00d5ec3aaf1422dca44f7d208f1b63ac40d66220d","abstract_canon_sha256":"8bb3166ef136342ee21dda20d8173c42fec0b8c4b7bffceae41c930bcb41dc5c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:19.310635Z","signature_b64":"vXG2B6SHNRBt9RTqBihVNqXJx27HwgQFowHLSNH+VmOT1RM2dNCvQIUmdNexiIMQbHXpeLFyQaX4BvZH4LGwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a42751e0ea6939b1dee544411bc3e3cbac06ac81f00dfbe4df4cb8a0f47d15a","last_reissued_at":"2026-05-17T23:59:19.310273Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:19.310273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constructions for the Elekes-Szab\\'o and Elekes-R\\'onyai problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Audie Warren, Frank de Zeeuw, Mehdi Makhul, Oliver Roche-Newton","submitted_at":"2018-12-03T10:40:54Z","abstract_excerpt":"We give a construction of a non-degenerate polynomial $F\\in \\mathbb R[x,y,z]$ and a set $A$ of cardinality $n$ such that $\\left|Z(F)\\cap (A \\times A \\times A) \\right| \\gg n^{\\frac{3}{2}}$, thus providing a new lower bound construction for the Elekes--Szab\\'o problem. We also give a related construction for the Elekes--R\\'onyai problem restricted to a subgraph. This consists of a polynomial $f\\in \\mathbb R[x,y]$ that is not additive or multiplicative, a set $A$ of size $n$, and a subset $P\\subset A\\times A$ of size $|P|\\gg n^{3/2}$ on which $f$ takes only $n$ distinct values."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00654","kind":"arxiv","version":1},"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":"1812.00654","created_at":"2026-05-17T23:59:19.310336+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.00654v1","created_at":"2026-05-17T23:59:19.310336+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00654","created_at":"2026-05-17T23:59:19.310336+00:00"},{"alias_kind":"pith_short_12","alias_value":"RJBHKHQOU2JZ","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"RJBHKHQOU2JZWHPO","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"RJBHKHQO","created_at":"2026-05-18T12:32:50.500415+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/RJBHKHQOU2JZWHPOKRCBDPB6HS","json":"https://pith.science/pith/RJBHKHQOU2JZWHPOKRCBDPB6HS.json","graph_json":"https://pith.science/api/pith-number/RJBHKHQOU2JZWHPOKRCBDPB6HS/graph.json","events_json":"https://pith.science/api/pith-number/RJBHKHQOU2JZWHPOKRCBDPB6HS/events.json","paper":"https://pith.science/paper/RJBHKHQO"},"agent_actions":{"view_html":"https://pith.science/pith/RJBHKHQOU2JZWHPOKRCBDPB6HS","download_json":"https://pith.science/pith/RJBHKHQOU2JZWHPOKRCBDPB6HS.json","view_paper":"https://pith.science/paper/RJBHKHQO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.00654&json=true","fetch_graph":"https://pith.science/api/pith-number/RJBHKHQOU2JZWHPOKRCBDPB6HS/graph.json","fetch_events":"https://pith.science/api/pith-number/RJBHKHQOU2JZWHPOKRCBDPB6HS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RJBHKHQOU2JZWHPOKRCBDPB6HS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RJBHKHQOU2JZWHPOKRCBDPB6HS/action/storage_attestation","attest_author":"https://pith.science/pith/RJBHKHQOU2JZWHPOKRCBDPB6HS/action/author_attestation","sign_citation":"https://pith.science/pith/RJBHKHQOU2JZWHPOKRCBDPB6HS/action/citation_signature","submit_replication":"https://pith.science/pith/RJBHKHQOU2JZWHPOKRCBDPB6HS/action/replication_record"}},"created_at":"2026-05-17T23:59:19.310336+00:00","updated_at":"2026-05-17T23:59:19.310336+00:00"}