{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QMC2WICB2QMGHW4SFF7YWJV3KR","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":"e43f9163e735aa5cf0fc94a75d373f3ed7d4e4f0a083b03e91994e0d0b4277aa","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-13T23:27:07Z","title_canon_sha256":"293950227f4e25cbc8922df9b5bfae5597ebeec8290ab026e5657e685e61cab7"},"schema_version":"1.0","source":{"id":"1212.3365","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3365","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3365v1","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3365","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"QMC2WICB2QMG","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QMC2WICB2QMGHW4S","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QMC2WICB","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:48ab0ae780a4599da880114024593835a5b3d1e83df92f0241c1413894c7f7b1","target":"graph","created_at":"2026-05-18T03:38:24Z","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":"Let $F(x,y)$ be a polynomial over the rationals. We show that if $F$ is not an expander (over the rationals) then it has a special multiplicative or additive form. For example if $F$ is a homogeneous non-expander polynomial then $F(x,y)=c(x+ay)^\\alpha$ or $F(x,y)=c(xy)^\\alpha .$ This is an extension of an earlier result of Elekes and R\\'onyai who described the structure of two-variate polynomials which are not expanders over the reals.","authors_text":"Jozsef Solymosi","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-13T23:27:07Z","title":"Expanding Polynomials over the rationals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3365","kind":"arxiv","version":1},"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":"sha256:0c04ffbd2e38641b23de7d95d0af5557f1aafc9d7df511852d7f0e540fc5841b","target":"record","created_at":"2026-05-18T03:38:24Z","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":"e43f9163e735aa5cf0fc94a75d373f3ed7d4e4f0a083b03e91994e0d0b4277aa","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-13T23:27:07Z","title_canon_sha256":"293950227f4e25cbc8922df9b5bfae5597ebeec8290ab026e5657e685e61cab7"},"schema_version":"1.0","source":{"id":"1212.3365","kind":"arxiv","version":1}},"canonical_sha256":"8305ab2041d41863db92297f8b26bb5468d500260ff0ee2635f4f7f856a8d82a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8305ab2041d41863db92297f8b26bb5468d500260ff0ee2635f4f7f856a8d82a","first_computed_at":"2026-05-18T03:38:24.865077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:24.865077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tomvJuL8VMCTPBnl047nmMnFnt3WKrgr3P1OogG0nHzgeFd+e1HnV5+HTkatkcbXFI+fazOqCIPEkss171UTAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:24.865589Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3365","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c04ffbd2e38641b23de7d95d0af5557f1aafc9d7df511852d7f0e540fc5841b","sha256:48ab0ae780a4599da880114024593835a5b3d1e83df92f0241c1413894c7f7b1"],"state_sha256":"93976f6608f048acbd79b90e4d03ff78f1085ce40327d352bf32bb977c14e252"}