{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:PPRMARLNAV3KOQSCCEKWXKVEDW","short_pith_number":"pith:PPRMARLN","schema_version":"1.0","canonical_sha256":"7be2c0456d0576a7424211156baaa41d9ec13b23dd015bf55c2c412eae0af67c","source":{"kind":"arxiv","id":"1302.5571","version":2},"attestation_state":"computed","paper":{"title":"Multiple recurrence for non-commuting transformations along rationally independent polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.DS","authors_text":"Nikos Frantzikinakis, Pavel Zorin-Kranich","submitted_at":"2013-02-22T12:38:58Z","abstract_excerpt":"We prove a multiple recurrence result for arbitrary measure-preserving transformations along polynomials in two variables of the form $m+p_i(n)$, with rationally independent $p_i$'s with zero constant term. This is in contrast to the single variable case, in which even double recurrence fails unless the transformations generate a virtually nilpotent group. The proof involves reduction to nilfactors and an equidistribution result on nilmanifolds."},"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":"1302.5571","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-22T12:38:58Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6f729cb694264650d87e3a268194884be0c4073097c368ac73add295687dbed8","abstract_canon_sha256":"f118e9e6bf3b8acdfa9265472d95526c1e7cf4c33441afe92d6a1420b3fed613"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:17.855898Z","signature_b64":"TPzsM3dBzBMagRI1YJHdK7dcTg/1ZFewEah8h6kqykhJ1D4hRlhzriJlXFRsLxD/bOuHPvoQSNUV07DiwjHdCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7be2c0456d0576a7424211156baaa41d9ec13b23dd015bf55c2c412eae0af67c","last_reissued_at":"2026-05-17T23:53:17.855158Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:17.855158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiple recurrence for non-commuting transformations along rationally independent polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.DS","authors_text":"Nikos Frantzikinakis, Pavel Zorin-Kranich","submitted_at":"2013-02-22T12:38:58Z","abstract_excerpt":"We prove a multiple recurrence result for arbitrary measure-preserving transformations along polynomials in two variables of the form $m+p_i(n)$, with rationally independent $p_i$'s with zero constant term. This is in contrast to the single variable case, in which even double recurrence fails unless the transformations generate a virtually nilpotent group. The proof involves reduction to nilfactors and an equidistribution result on nilmanifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5571","kind":"arxiv","version":2},"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":"1302.5571","created_at":"2026-05-17T23:53:17.855273+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.5571v2","created_at":"2026-05-17T23:53:17.855273+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5571","created_at":"2026-05-17T23:53:17.855273+00:00"},{"alias_kind":"pith_short_12","alias_value":"PPRMARLNAV3K","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PPRMARLNAV3KOQSC","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PPRMARLN","created_at":"2026-05-18T12:27:54.935989+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/PPRMARLNAV3KOQSCCEKWXKVEDW","json":"https://pith.science/pith/PPRMARLNAV3KOQSCCEKWXKVEDW.json","graph_json":"https://pith.science/api/pith-number/PPRMARLNAV3KOQSCCEKWXKVEDW/graph.json","events_json":"https://pith.science/api/pith-number/PPRMARLNAV3KOQSCCEKWXKVEDW/events.json","paper":"https://pith.science/paper/PPRMARLN"},"agent_actions":{"view_html":"https://pith.science/pith/PPRMARLNAV3KOQSCCEKWXKVEDW","download_json":"https://pith.science/pith/PPRMARLNAV3KOQSCCEKWXKVEDW.json","view_paper":"https://pith.science/paper/PPRMARLN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.5571&json=true","fetch_graph":"https://pith.science/api/pith-number/PPRMARLNAV3KOQSCCEKWXKVEDW/graph.json","fetch_events":"https://pith.science/api/pith-number/PPRMARLNAV3KOQSCCEKWXKVEDW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PPRMARLNAV3KOQSCCEKWXKVEDW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PPRMARLNAV3KOQSCCEKWXKVEDW/action/storage_attestation","attest_author":"https://pith.science/pith/PPRMARLNAV3KOQSCCEKWXKVEDW/action/author_attestation","sign_citation":"https://pith.science/pith/PPRMARLNAV3KOQSCCEKWXKVEDW/action/citation_signature","submit_replication":"https://pith.science/pith/PPRMARLNAV3KOQSCCEKWXKVEDW/action/replication_record"}},"created_at":"2026-05-17T23:53:17.855273+00:00","updated_at":"2026-05-17T23:53:17.855273+00:00"}