{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WVEFLE65DAYQ7OH5HQDVHRPHBV","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":"e13b484dca391d7ff49edab89d5abbfe934abbc58b72793c60b178904bb2174e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-24T16:10:04Z","title_canon_sha256":"4c259eaaa057a02574355e017b96a41cf0aae4b610cb27c0e3fe6139b284baff"},"schema_version":"1.0","source":{"id":"1601.06404","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06404","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06404v2","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06404","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"WVEFLE65DAYQ","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WVEFLE65DAYQ7OH5","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WVEFLE65","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:c2bdb461da8a4dca791e9f8cc4aa878973f7f1a4a829135f045a092041bd4c04","target":"graph","created_at":"2026-05-18T01:18:13Z","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 give an overview of recent progress around a problem introduced by Elekes and R\\'onyai. The prototype problem is to show that a polynomial $f\\in \\mathbb{R}[x,y]$ has a large image on a Cartesian product $A\\times B\\subset \\mathbb{R}^2$, unless $f$ has a group-related special form. We discuss a number of variants and generalizations. This includes the Elekes-Szab\\'o problem, which generalizes the Elekes-R\\'onyai problem to a question about an upper bound on the intersection of an algebraic surface with a Cartesian product, and curve variants, where we ask the same questions for Cartesian prod","authors_text":"Frank de Zeeuw","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-24T16:10:04Z","title":"A survey of Elekes-R\\'onyai-type problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06404","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":"sha256:6905e002caec6efee8009fdd21ae1ccdff5e1b7794b181ed7cb4b0ad35893a88","target":"record","created_at":"2026-05-18T01:18:13Z","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":"e13b484dca391d7ff49edab89d5abbfe934abbc58b72793c60b178904bb2174e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-24T16:10:04Z","title_canon_sha256":"4c259eaaa057a02574355e017b96a41cf0aae4b610cb27c0e3fe6139b284baff"},"schema_version":"1.0","source":{"id":"1601.06404","kind":"arxiv","version":2}},"canonical_sha256":"b5485593dd18310fb8fd3c0753c5e70d72acea915ed25f2e897a082b27d1a517","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5485593dd18310fb8fd3c0753c5e70d72acea915ed25f2e897a082b27d1a517","first_computed_at":"2026-05-18T01:18:13.871862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:13.871862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"muJh4lB9oPoyn7sK0YkfZYImd0PvXaAZRvVWmndz2rZQnUMJWMjjxrayLjuTYWUrsJgL7HFWsa15vGsZYpZpAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:13.872576Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.06404","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6905e002caec6efee8009fdd21ae1ccdff5e1b7794b181ed7cb4b0ad35893a88","sha256:c2bdb461da8a4dca791e9f8cc4aa878973f7f1a4a829135f045a092041bd4c04"],"state_sha256":"324d9a80403c26cbdb71dc888a961b9c3a58c7abc8b1341be971d585985ce9f7"}