{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:5B3XEUKRGCOL5I7EI6Q6FN4TRH","short_pith_number":"pith:5B3XEUKR","schema_version":"1.0","canonical_sha256":"e877725151309cbea3e447a1e2b79389dde0eb788f55532d428574f2bdd059bb","source":{"kind":"arxiv","id":"1904.11123","version":1},"attestation_state":"computed","paper":{"title":"Polynomial Roth theorems on sets of fractional dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Malabika Pramanik, Robert Fraser, Shaoming Guo","submitted_at":"2019-04-25T02:05:12Z","abstract_excerpt":"Let $E\\subset \\mathbb{R}$ be a closed set of Hausdorff dimension $\\alpha\\in (0, 1)$. Let $P: \\mathbb{R}\\to \\mathbb{R}$ be a polynomial without a constant term whose degree is bigger than one. We prove that if $E$ supports a probability measure satisfying certain dimension condition and Fourier decay condition, then $E$ contains three points $x, x+t, x+P(t)$ for some $t>0$. Our result extends the one of Laba and the third author to the polynomial setting, under the same assumption. It also gives an affirmative answer to a question in Henriot, Laba and the third author."},"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":"1904.11123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-04-25T02:05:12Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f97d06b8239c16f176591501f42f547d46de4862ada1739d27393733ccfd2fa0","abstract_canon_sha256":"ad13c70be167ff28692547cde8d3f633598e45b813fd4531ff6f6fdc39e4992f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:45.731406Z","signature_b64":"DE7kLWyMDOup4PG3q/h8pcAEnHNQulA+pHu2N3LakhOMAzyHJLC9CbUQE/0znmQHOx/F21x7ouK4IL7AW3IAAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e877725151309cbea3e447a1e2b79389dde0eb788f55532d428574f2bdd059bb","last_reissued_at":"2026-05-17T23:47:45.730954Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:45.730954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomial Roth theorems on sets of fractional dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Malabika Pramanik, Robert Fraser, Shaoming Guo","submitted_at":"2019-04-25T02:05:12Z","abstract_excerpt":"Let $E\\subset \\mathbb{R}$ be a closed set of Hausdorff dimension $\\alpha\\in (0, 1)$. Let $P: \\mathbb{R}\\to \\mathbb{R}$ be a polynomial without a constant term whose degree is bigger than one. We prove that if $E$ supports a probability measure satisfying certain dimension condition and Fourier decay condition, then $E$ contains three points $x, x+t, x+P(t)$ for some $t>0$. Our result extends the one of Laba and the third author to the polynomial setting, under the same assumption. It also gives an affirmative answer to a question in Henriot, Laba and the third author."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11123","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":"1904.11123","created_at":"2026-05-17T23:47:45.731020+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.11123v1","created_at":"2026-05-17T23:47:45.731020+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11123","created_at":"2026-05-17T23:47:45.731020+00:00"},{"alias_kind":"pith_short_12","alias_value":"5B3XEUKRGCOL","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"5B3XEUKRGCOL5I7E","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"5B3XEUKR","created_at":"2026-05-18T12:33:10.108867+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/5B3XEUKRGCOL5I7EI6Q6FN4TRH","json":"https://pith.science/pith/5B3XEUKRGCOL5I7EI6Q6FN4TRH.json","graph_json":"https://pith.science/api/pith-number/5B3XEUKRGCOL5I7EI6Q6FN4TRH/graph.json","events_json":"https://pith.science/api/pith-number/5B3XEUKRGCOL5I7EI6Q6FN4TRH/events.json","paper":"https://pith.science/paper/5B3XEUKR"},"agent_actions":{"view_html":"https://pith.science/pith/5B3XEUKRGCOL5I7EI6Q6FN4TRH","download_json":"https://pith.science/pith/5B3XEUKRGCOL5I7EI6Q6FN4TRH.json","view_paper":"https://pith.science/paper/5B3XEUKR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.11123&json=true","fetch_graph":"https://pith.science/api/pith-number/5B3XEUKRGCOL5I7EI6Q6FN4TRH/graph.json","fetch_events":"https://pith.science/api/pith-number/5B3XEUKRGCOL5I7EI6Q6FN4TRH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5B3XEUKRGCOL5I7EI6Q6FN4TRH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5B3XEUKRGCOL5I7EI6Q6FN4TRH/action/storage_attestation","attest_author":"https://pith.science/pith/5B3XEUKRGCOL5I7EI6Q6FN4TRH/action/author_attestation","sign_citation":"https://pith.science/pith/5B3XEUKRGCOL5I7EI6Q6FN4TRH/action/citation_signature","submit_replication":"https://pith.science/pith/5B3XEUKRGCOL5I7EI6Q6FN4TRH/action/replication_record"}},"created_at":"2026-05-17T23:47:45.731020+00:00","updated_at":"2026-05-17T23:47:45.731020+00:00"}