{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:XFMK4I25BXTTYWBB4HR25TI5QZ","short_pith_number":"pith:XFMK4I25","schema_version":"1.0","canonical_sha256":"b958ae235d0de73c5821e1e3aecd1d866a35ef6d07c07d0d0b7a7d69edc07e99","source":{"kind":"arxiv","id":"2407.08338","version":1},"attestation_state":"computed","paper":{"title":"Bounds in a popular multidimensional nonlinear Roth theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Sarah Peluse, Sean Prendiville, Xuancheng Shao","submitted_at":"2024-07-11T09:40:55Z","abstract_excerpt":"A nonlinear version of Roth's theorem states that dense sets of integers contain configurations of the form $x$, $x+d$, $x+d^2$. We obtain a multidimensional version of this result, which can be regarded as a first step towards effectivising those cases of the multidimensional polynomial Szemer\\'edi theorem involving polynomials with distinct degrees. In addition, we prove an effective ``popular'' version of this result, showing that every dense set has some non-zero $d$ such that the number of configurations with difference parameter $d$ is almost optimal. Perhaps surprisingly, the quantitati"},"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":"2407.08338","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-07-11T09:40:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"cb054380eae9da690171fab107e09109238f48426ca9abc1d73f939f699e7a16","abstract_canon_sha256":"eb1b03f6f9ace48a4ce30b7d8f10d5bf4fb878ea4089b5ef187f2a2529d5fade"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:42:46.955862Z","signature_b64":"KBFAzW3cpqbvyYQ9SqObG/2xWlPQhKb9A8UtN8I63HM0ZWlIn3P4KdCUU0AQnkVczprnSIzl7CC40EheqBatDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b958ae235d0de73c5821e1e3aecd1d866a35ef6d07c07d0d0b7a7d69edc07e99","last_reissued_at":"2026-07-05T08:42:46.955392Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:42:46.955392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds in a popular multidimensional nonlinear Roth theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Sarah Peluse, Sean Prendiville, Xuancheng Shao","submitted_at":"2024-07-11T09:40:55Z","abstract_excerpt":"A nonlinear version of Roth's theorem states that dense sets of integers contain configurations of the form $x$, $x+d$, $x+d^2$. We obtain a multidimensional version of this result, which can be regarded as a first step towards effectivising those cases of the multidimensional polynomial Szemer\\'edi theorem involving polynomials with distinct degrees. In addition, we prove an effective ``popular'' version of this result, showing that every dense set has some non-zero $d$ such that the number of configurations with difference parameter $d$ is almost optimal. Perhaps surprisingly, the quantitati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.08338","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.08338/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2407.08338","created_at":"2026-07-05T08:42:46.955449+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.08338v1","created_at":"2026-07-05T08:42:46.955449+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.08338","created_at":"2026-07-05T08:42:46.955449+00:00"},{"alias_kind":"pith_short_12","alias_value":"XFMK4I25BXTT","created_at":"2026-07-05T08:42:46.955449+00:00"},{"alias_kind":"pith_short_16","alias_value":"XFMK4I25BXTTYWBB","created_at":"2026-07-05T08:42:46.955449+00:00"},{"alias_kind":"pith_short_8","alias_value":"XFMK4I25","created_at":"2026-07-05T08:42:46.955449+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.04887","citing_title":"Uniform nonlinear Szemer\\'{e}di theorem for corners in finite fields","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XFMK4I25BXTTYWBB4HR25TI5QZ","json":"https://pith.science/pith/XFMK4I25BXTTYWBB4HR25TI5QZ.json","graph_json":"https://pith.science/api/pith-number/XFMK4I25BXTTYWBB4HR25TI5QZ/graph.json","events_json":"https://pith.science/api/pith-number/XFMK4I25BXTTYWBB4HR25TI5QZ/events.json","paper":"https://pith.science/paper/XFMK4I25"},"agent_actions":{"view_html":"https://pith.science/pith/XFMK4I25BXTTYWBB4HR25TI5QZ","download_json":"https://pith.science/pith/XFMK4I25BXTTYWBB4HR25TI5QZ.json","view_paper":"https://pith.science/paper/XFMK4I25","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.08338&json=true","fetch_graph":"https://pith.science/api/pith-number/XFMK4I25BXTTYWBB4HR25TI5QZ/graph.json","fetch_events":"https://pith.science/api/pith-number/XFMK4I25BXTTYWBB4HR25TI5QZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XFMK4I25BXTTYWBB4HR25TI5QZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XFMK4I25BXTTYWBB4HR25TI5QZ/action/storage_attestation","attest_author":"https://pith.science/pith/XFMK4I25BXTTYWBB4HR25TI5QZ/action/author_attestation","sign_citation":"https://pith.science/pith/XFMK4I25BXTTYWBB4HR25TI5QZ/action/citation_signature","submit_replication":"https://pith.science/pith/XFMK4I25BXTTYWBB4HR25TI5QZ/action/replication_record"}},"created_at":"2026-07-05T08:42:46.955449+00:00","updated_at":"2026-07-05T08:42:46.955449+00:00"}