{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:D5MYJYIFNT5VL6T5VV2F3XFD5X","short_pith_number":"pith:D5MYJYIF","schema_version":"1.0","canonical_sha256":"1f5984e1056cfb55fa7dad745ddca3edd7ec2827f77f65d460052454bcba34d0","source":{"kind":"arxiv","id":"1210.4659","version":1},"attestation_state":"computed","paper":{"title":"Polynomial configurations in the primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Julia Wolf, Thai Hoang Le","submitted_at":"2012-10-17T07:53:45Z","abstract_excerpt":"The Bergelson-Leibman theorem states that if P_1, ..., P_k are polynomials with integer coefficients, then any subset of the integers of positive upper density contains a polynomial configuration x+P_1(m), ..., x+P_k(m), where x,m are integers. Various generalizations of this theorem are known. Wooley and Ziegler showed that the variable m can in fact be taken to be a prime minus 1, and Tao and Ziegler showed that the Bergelson-Leibman theorem holds for subsets of the primes of positive relative upper density. Here we prove a hybrid of the latter two results, namely that the step m in the Tao-"},"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":"1210.4659","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-17T07:53:45Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"d871ac5d425d91faaa2682f601313b00c43e08e1551b958957d83b00150120ac","abstract_canon_sha256":"646e99661d41a94fb1f40b1f75ba38ce788136858046c4bff6fc895d153e8b20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:28.911557Z","signature_b64":"F811pZa6lVn0IW2Ji8zuhtFKvErHfr6bEejj3KCdZprKPZEfZ0VD1veUav5TGSO7aHa6jQb+fxlVA9KS6zzlDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f5984e1056cfb55fa7dad745ddca3edd7ec2827f77f65d460052454bcba34d0","last_reissued_at":"2026-05-17T23:43:28.910887Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:28.910887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomial configurations in the primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Julia Wolf, Thai Hoang Le","submitted_at":"2012-10-17T07:53:45Z","abstract_excerpt":"The Bergelson-Leibman theorem states that if P_1, ..., P_k are polynomials with integer coefficients, then any subset of the integers of positive upper density contains a polynomial configuration x+P_1(m), ..., x+P_k(m), where x,m are integers. Various generalizations of this theorem are known. Wooley and Ziegler showed that the variable m can in fact be taken to be a prime minus 1, and Tao and Ziegler showed that the Bergelson-Leibman theorem holds for subsets of the primes of positive relative upper density. Here we prove a hybrid of the latter two results, namely that the step m in the Tao-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4659","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":"1210.4659","created_at":"2026-05-17T23:43:28.910989+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.4659v1","created_at":"2026-05-17T23:43:28.910989+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4659","created_at":"2026-05-17T23:43:28.910989+00:00"},{"alias_kind":"pith_short_12","alias_value":"D5MYJYIFNT5V","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"D5MYJYIFNT5VL6T5","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"D5MYJYIF","created_at":"2026-05-18T12:27:01.376967+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/D5MYJYIFNT5VL6T5VV2F3XFD5X","json":"https://pith.science/pith/D5MYJYIFNT5VL6T5VV2F3XFD5X.json","graph_json":"https://pith.science/api/pith-number/D5MYJYIFNT5VL6T5VV2F3XFD5X/graph.json","events_json":"https://pith.science/api/pith-number/D5MYJYIFNT5VL6T5VV2F3XFD5X/events.json","paper":"https://pith.science/paper/D5MYJYIF"},"agent_actions":{"view_html":"https://pith.science/pith/D5MYJYIFNT5VL6T5VV2F3XFD5X","download_json":"https://pith.science/pith/D5MYJYIFNT5VL6T5VV2F3XFD5X.json","view_paper":"https://pith.science/paper/D5MYJYIF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.4659&json=true","fetch_graph":"https://pith.science/api/pith-number/D5MYJYIFNT5VL6T5VV2F3XFD5X/graph.json","fetch_events":"https://pith.science/api/pith-number/D5MYJYIFNT5VL6T5VV2F3XFD5X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D5MYJYIFNT5VL6T5VV2F3XFD5X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D5MYJYIFNT5VL6T5VV2F3XFD5X/action/storage_attestation","attest_author":"https://pith.science/pith/D5MYJYIFNT5VL6T5VV2F3XFD5X/action/author_attestation","sign_citation":"https://pith.science/pith/D5MYJYIFNT5VL6T5VV2F3XFD5X/action/citation_signature","submit_replication":"https://pith.science/pith/D5MYJYIFNT5VL6T5VV2F3XFD5X/action/replication_record"}},"created_at":"2026-05-17T23:43:28.910989+00:00","updated_at":"2026-05-17T23:43:28.910989+00:00"}