{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:D5MYJYIFNT5VL6T5VV2F3XFD5X","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":"646e99661d41a94fb1f40b1f75ba38ce788136858046c4bff6fc895d153e8b20","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-17T07:53:45Z","title_canon_sha256":"d871ac5d425d91faaa2682f601313b00c43e08e1551b958957d83b00150120ac"},"schema_version":"1.0","source":{"id":"1210.4659","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4659","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4659v1","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4659","created_at":"2026-05-17T23:43:28Z"},{"alias_kind":"pith_short_12","alias_value":"D5MYJYIFNT5V","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D5MYJYIFNT5VL6T5","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D5MYJYIF","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:fdd41818a49bb82751e73602d5bf5ff9701f70524adda345bf20a8df6b45c44c","target":"graph","created_at":"2026-05-17T23:43:28Z","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":"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-","authors_text":"Julia Wolf, Thai Hoang Le","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-17T07:53:45Z","title":"Polynomial configurations in the primes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4659","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":"sha256:27ad4efb41ef435ab0ee9cc6e4f904f3d3cae1f01c4e2add04d2bb8815de6a50","target":"record","created_at":"2026-05-17T23:43:28Z","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":"646e99661d41a94fb1f40b1f75ba38ce788136858046c4bff6fc895d153e8b20","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-17T07:53:45Z","title_canon_sha256":"d871ac5d425d91faaa2682f601313b00c43e08e1551b958957d83b00150120ac"},"schema_version":"1.0","source":{"id":"1210.4659","kind":"arxiv","version":1}},"canonical_sha256":"1f5984e1056cfb55fa7dad745ddca3edd7ec2827f77f65d460052454bcba34d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f5984e1056cfb55fa7dad745ddca3edd7ec2827f77f65d460052454bcba34d0","first_computed_at":"2026-05-17T23:43:28.910887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:28.910887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F811pZa6lVn0IW2Ji8zuhtFKvErHfr6bEejj3KCdZprKPZEfZ0VD1veUav5TGSO7aHa6jQb+fxlVA9KS6zzlDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:28.911557Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4659","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27ad4efb41ef435ab0ee9cc6e4f904f3d3cae1f01c4e2add04d2bb8815de6a50","sha256:fdd41818a49bb82751e73602d5bf5ff9701f70524adda345bf20a8df6b45c44c"],"state_sha256":"e164ffecd5f2f26a3b61e2132b00bbcf4b07cf678c379d9a4a008d7e83787bfc"}