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(2021), no. 11, 46 pp","work_id":"577aef4d-3b7e-445a-a305-746c19a3301f","year":2021}],"snapshot_sha256":"1bce3b2c848b743cea8f9599288e690f5d559825abbe9ec1e067832688a88f4f"},"source":{"id":"2605.16216","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T18:27:12.380056Z","id":"9809a34e-c3d3-4d1c-8a65-ee134b8e1583","model_set":{"reader":"grok-4.3"},"one_line_summary":"Extends Furstenberg-Sárközy to general intersective polynomials h via uniform arithmetic level-d inequality, yielding the best known quasipolynomial density bound.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"For any intersective polynomial h the largest subset of {1,...,X} without nonzero h(n) differences has a quasipolynomial upper bound on size.","strongest_claim":"We adapt their method to general intersective polynomials h∈Z[x] and obtain an analogous quasipolynomial upper bound for the largest subset of {1,2,…,X} whose difference set contains no nonzero element of the form h(n) with n∈Z.","weakest_assumption":"The arithmetic level-d inequality remains effective uniformly across all auxiliary polynomials arising in the iteration."}},"verdict_id":"9809a34e-c3d3-4d1c-8a65-ee134b8e1583"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6aff7eaf63f953bc175c857423fd8d04fe6e733a0162f84315c91b44a8b30ed4","target":"record","created_at":"2026-05-20T00:01:58Z","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":"b081ffbaa491fd57f996191f8ae2b4b6b2af9ae84383a348a8c8b110e9ac13b0","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-15T17:29:24Z","title_canon_sha256":"ada7c1b45f35afc48b4a46069770661ce3eba1b174fae53ff7e215eb9e09204c"},"schema_version":"1.0","source":{"id":"2605.16216","kind":"arxiv","version":1}},"canonical_sha256":"1c8ea46b51d940e690628e2174852eb72163d1dcb6034b166b5282e6afdeaa59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c8ea46b51d940e690628e2174852eb72163d1dcb6034b166b5282e6afdeaa59","first_computed_at":"2026-05-20T00:01:58.498795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:58.498795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cep7n6UhkeaNrXTWic+sk6pR3WWZhLV9p9GWl3BSGL17JYKJdFx6/U8SGtGF8XBefLB3iQRsSB6jkPJETA2VDA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:58.499674Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16216","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6aff7eaf63f953bc175c857423fd8d04fe6e733a0162f84315c91b44a8b30ed4","sha256:51afa09e162b7b3846f1ed8862e10af27a55130d3766ff53038960cd64db830d"],"state_sha256":"c2571d0894dffc814fa5b4db4a4ba717677803a8fb003cc6d335138a528b2ec9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3P2R6WiUSagAOpYBebv8PLjeRG1PEDng3yg+bSxrkxCl2ffST1Z7uOx3z+KY0WuKBS3Ufuco0K3JJqmZycjvDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T11:04:43.670954Z","bundle_sha256":"cc3f84179da283dc6d6938baf2e2117b1c64247b88fffe13d7eb14a3ec967fde"}}