{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:IT7CPFTOYYNKJLPNUC4MGXY5UX","short_pith_number":"pith:IT7CPFTO","schema_version":"1.0","canonical_sha256":"44fe27966ec61aa4adeda0b8c35f1da5f0d65744854952b51f38ab2a7fe99425","source":{"kind":"arxiv","id":"1301.5122","version":1},"attestation_state":"computed","paper":{"title":"On a conjecture of Rudin on squares in Arithmetic Progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Enrique Gonz\\'alez-Jim\\'enez, Xavier Xarles","submitted_at":"2013-01-22T09:53:02Z","abstract_excerpt":"Let Q(N;q,a) denotes the number of squares in the arithmetic progression qn+a, for n=0, 1,...,N-1, and let Q(N) be the maximum of Q(N;q,a) over all non-trivial arithmetic progressions qn + a. Rudin's conjecture asserts that Q(N)=O(Sqrt(N)), and in its stronger form that Q(N)=Q(N;24,1) if N=> 6. We prove the conjecture above for 6<=N<=52. We even prove that the arithmetic progression 24n+1 is the only one, up to equivalence, that contains Q(N) squares for the values of N such that Q(N) increases, for 7<=N<=52 (hence, for N=8,13,16,23,27,36,41 and 52). This allow us to assert, what we have calle"},"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":"1301.5122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-22T09:53:02Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"69ca49fb5e5c13eb76229bf18ea91dc5fc06f5b9e69098f88c91e1965134ac5d","abstract_canon_sha256":"7f62836f9854af2ac88b45f3b96ea59ca3635c0b78a0a283259922eb88ddcbf8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:58.997077Z","signature_b64":"R20VpUXZ/TWnqfNo9aLoPvYhyisuelrZcWv/XwLTeUwJcQ+bxybl4VkBc2LkRZQbXrrnAOKgSe+inkS2xeK0CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44fe27966ec61aa4adeda0b8c35f1da5f0d65744854952b51f38ab2a7fe99425","last_reissued_at":"2026-05-18T02:37:58.996729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:58.996729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a conjecture of Rudin on squares in Arithmetic Progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Enrique Gonz\\'alez-Jim\\'enez, Xavier Xarles","submitted_at":"2013-01-22T09:53:02Z","abstract_excerpt":"Let Q(N;q,a) denotes the number of squares in the arithmetic progression qn+a, for n=0, 1,...,N-1, and let Q(N) be the maximum of Q(N;q,a) over all non-trivial arithmetic progressions qn + a. Rudin's conjecture asserts that Q(N)=O(Sqrt(N)), and in its stronger form that Q(N)=Q(N;24,1) if N=> 6. We prove the conjecture above for 6<=N<=52. We even prove that the arithmetic progression 24n+1 is the only one, up to equivalence, that contains Q(N) squares for the values of N such that Q(N) increases, for 7<=N<=52 (hence, for N=8,13,16,23,27,36,41 and 52). This allow us to assert, what we have calle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5122","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":"1301.5122","created_at":"2026-05-18T02:37:58.996778+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.5122v1","created_at":"2026-05-18T02:37:58.996778+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5122","created_at":"2026-05-18T02:37:58.996778+00:00"},{"alias_kind":"pith_short_12","alias_value":"IT7CPFTOYYNK","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"IT7CPFTOYYNKJLPN","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"IT7CPFTO","created_at":"2026-05-18T12:27:49.015174+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/IT7CPFTOYYNKJLPNUC4MGXY5UX","json":"https://pith.science/pith/IT7CPFTOYYNKJLPNUC4MGXY5UX.json","graph_json":"https://pith.science/api/pith-number/IT7CPFTOYYNKJLPNUC4MGXY5UX/graph.json","events_json":"https://pith.science/api/pith-number/IT7CPFTOYYNKJLPNUC4MGXY5UX/events.json","paper":"https://pith.science/paper/IT7CPFTO"},"agent_actions":{"view_html":"https://pith.science/pith/IT7CPFTOYYNKJLPNUC4MGXY5UX","download_json":"https://pith.science/pith/IT7CPFTOYYNKJLPNUC4MGXY5UX.json","view_paper":"https://pith.science/paper/IT7CPFTO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.5122&json=true","fetch_graph":"https://pith.science/api/pith-number/IT7CPFTOYYNKJLPNUC4MGXY5UX/graph.json","fetch_events":"https://pith.science/api/pith-number/IT7CPFTOYYNKJLPNUC4MGXY5UX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IT7CPFTOYYNKJLPNUC4MGXY5UX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IT7CPFTOYYNKJLPNUC4MGXY5UX/action/storage_attestation","attest_author":"https://pith.science/pith/IT7CPFTOYYNKJLPNUC4MGXY5UX/action/author_attestation","sign_citation":"https://pith.science/pith/IT7CPFTOYYNKJLPNUC4MGXY5UX/action/citation_signature","submit_replication":"https://pith.science/pith/IT7CPFTOYYNKJLPNUC4MGXY5UX/action/replication_record"}},"created_at":"2026-05-18T02:37:58.996778+00:00","updated_at":"2026-05-18T02:37:58.996778+00:00"}