{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:B7ZWZBRWYRD6GVBNKBLOTESNG4","short_pith_number":"pith:B7ZWZBRW","schema_version":"1.0","canonical_sha256":"0ff36c8636c447e3542d5056e9924d372c037d7774ad82eb82c42bb012a3c52b","source":{"kind":"arxiv","id":"2301.06970","version":4},"attestation_state":"computed","paper":{"title":"Binary Cubic Forms and Rational Cube Sum Problem","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"B. Sury, Dipramit Majumdar, Somnath Jha","submitted_at":"2023-01-17T15:44:20Z","abstract_excerpt":"In this note, we use integral binary cubic forms to study the rational cube sum problem. We prove (unconditionally) that for any positive integer $d$, infinitely many primes in each of the residue classes $ 1 \\pmod {9d}$ as well as $ -1 \\pmod {9d}$, are sums of two rational cubes. Among other results, we prove that every non-zero residue class $a \\pmod {q}$, for any prime $q$, contains infinitely many primes which are sums of two rational cubes. Further, for an arbitrary integer $N$, we show there are infinitely many primes $p$ in each of the residue classes $ 8 \\pmod 9$ and $1 \\pmod 9$, such "},"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":"2301.06970","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2023-01-17T15:44:20Z","cross_cats_sorted":[],"title_canon_sha256":"5974b9781fe5f0444ca06150e8f29acf62e47c825b2e1fc6e53ad3a84a43d235","abstract_canon_sha256":"92fde3abca87f46b46b19d58904a0517b31ad1d4f513f36ad57e7f1301acf632"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:25:26.985995Z","signature_b64":"aeQpBqqfU8BmLAHc1yiZLWTU3xx9OPyTux/m0yfqQKmUH9oGC6PExmQi7CQqT4mtXSGt+KGKrNx2ztsB+vE+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ff36c8636c447e3542d5056e9924d372c037d7774ad82eb82c42bb012a3c52b","last_reissued_at":"2026-07-05T08:25:26.985615Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:25:26.985615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Binary Cubic Forms and Rational Cube Sum Problem","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"B. Sury, Dipramit Majumdar, Somnath Jha","submitted_at":"2023-01-17T15:44:20Z","abstract_excerpt":"In this note, we use integral binary cubic forms to study the rational cube sum problem. We prove (unconditionally) that for any positive integer $d$, infinitely many primes in each of the residue classes $ 1 \\pmod {9d}$ as well as $ -1 \\pmod {9d}$, are sums of two rational cubes. Among other results, we prove that every non-zero residue class $a \\pmod {q}$, for any prime $q$, contains infinitely many primes which are sums of two rational cubes. Further, for an arbitrary integer $N$, we show there are infinitely many primes $p$ in each of the residue classes $ 8 \\pmod 9$ and $1 \\pmod 9$, such "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.06970","kind":"arxiv","version":4},"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/2301.06970/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":"2301.06970","created_at":"2026-07-05T08:25:26.985676+00:00"},{"alias_kind":"arxiv_version","alias_value":"2301.06970v4","created_at":"2026-07-05T08:25:26.985676+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.06970","created_at":"2026-07-05T08:25:26.985676+00:00"},{"alias_kind":"pith_short_12","alias_value":"B7ZWZBRWYRD6","created_at":"2026-07-05T08:25:26.985676+00:00"},{"alias_kind":"pith_short_16","alias_value":"B7ZWZBRWYRD6GVBN","created_at":"2026-07-05T08:25:26.985676+00:00"},{"alias_kind":"pith_short_8","alias_value":"B7ZWZBRW","created_at":"2026-07-05T08:25:26.985676+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.13022","citing_title":"Relative $p$-class groups and $p$-Selmer groups","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B7ZWZBRWYRD6GVBNKBLOTESNG4","json":"https://pith.science/pith/B7ZWZBRWYRD6GVBNKBLOTESNG4.json","graph_json":"https://pith.science/api/pith-number/B7ZWZBRWYRD6GVBNKBLOTESNG4/graph.json","events_json":"https://pith.science/api/pith-number/B7ZWZBRWYRD6GVBNKBLOTESNG4/events.json","paper":"https://pith.science/paper/B7ZWZBRW"},"agent_actions":{"view_html":"https://pith.science/pith/B7ZWZBRWYRD6GVBNKBLOTESNG4","download_json":"https://pith.science/pith/B7ZWZBRWYRD6GVBNKBLOTESNG4.json","view_paper":"https://pith.science/paper/B7ZWZBRW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2301.06970&json=true","fetch_graph":"https://pith.science/api/pith-number/B7ZWZBRWYRD6GVBNKBLOTESNG4/graph.json","fetch_events":"https://pith.science/api/pith-number/B7ZWZBRWYRD6GVBNKBLOTESNG4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B7ZWZBRWYRD6GVBNKBLOTESNG4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B7ZWZBRWYRD6GVBNKBLOTESNG4/action/storage_attestation","attest_author":"https://pith.science/pith/B7ZWZBRWYRD6GVBNKBLOTESNG4/action/author_attestation","sign_citation":"https://pith.science/pith/B7ZWZBRWYRD6GVBNKBLOTESNG4/action/citation_signature","submit_replication":"https://pith.science/pith/B7ZWZBRWYRD6GVBNKBLOTESNG4/action/replication_record"}},"created_at":"2026-07-05T08:25:26.985676+00:00","updated_at":"2026-07-05T08:25:26.985676+00:00"}