{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LLQVQE6JVMZRGR6UMTPJH5KFLP","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":"b7d5631ad208eea68dc1511ad6f3e6396d03e06e6b406188574c18bfef0c8492","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-19T22:25:17Z","title_canon_sha256":"bbbd542f5e92cba9423fe1a052ada49a03cfe5d866368a6c021dc2ba84a6ecee"},"schema_version":"1.0","source":{"id":"1310.5275","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5275","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5275v4","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5275","created_at":"2026-05-18T01:37:08Z"},{"alias_kind":"pith_short_12","alias_value":"LLQVQE6JVMZR","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LLQVQE6JVMZRGR6U","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LLQVQE6J","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:268d0f8a0f1bac5b460b89d37dc5d03b637e5b1bdd38cbf7fe87e845218904b0","target":"graph","created_at":"2026-05-18T01:37:08Z","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 provide upper bounds on the density of a symmetric generalized arithmetic progression lacking nonzero elements of the form h(n) for natural numbers n, or h(p) with p prime, for appropriate polynomials h with integer coefficients. The prime variant can be interpreted as a multi-dimensional, polynomial extension of Linnik's Theorem. This version is a revision of the published version. Most notably, the properness hypotheses have been removed from Theorems 2 and 3, and the numerology in Theorem 2 has been improved.","authors_text":"Alex Rice, Ernie Croot, Neil Lyall","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-19T22:25:17Z","title":"Polynomials and Primes in Generalized Arithmetic Progressions (Revised Version)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5275","kind":"arxiv","version":4},"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":"sha256:8799f096b358e3f807db9c9f57ac6f8e4d788f4f6aa676b6167de415651af821","target":"record","created_at":"2026-05-18T01:37:08Z","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":"b7d5631ad208eea68dc1511ad6f3e6396d03e06e6b406188574c18bfef0c8492","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-19T22:25:17Z","title_canon_sha256":"bbbd542f5e92cba9423fe1a052ada49a03cfe5d866368a6c021dc2ba84a6ecee"},"schema_version":"1.0","source":{"id":"1310.5275","kind":"arxiv","version":4}},"canonical_sha256":"5ae15813c9ab331347d464de93f5455bf2449a4d14506a492b70df6b90b53ace","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ae15813c9ab331347d464de93f5455bf2449a4d14506a492b70df6b90b53ace","first_computed_at":"2026-05-18T01:37:08.026825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:08.026825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9JSO6Blln9YSk2sgWaU3jAwWzW/oSKKSlkqLbNbfcReSLk9eCb0RkmuBO94eU2BbTO3O5S2//D5WyZeq+uWSAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:08.027575Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.5275","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8799f096b358e3f807db9c9f57ac6f8e4d788f4f6aa676b6167de415651af821","sha256:268d0f8a0f1bac5b460b89d37dc5d03b637e5b1bdd38cbf7fe87e845218904b0"],"state_sha256":"7c2395e8d056ceeff21989adbad08ed1d067220c03ff2c7fde788ecf48ff1d16"}