{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:NS3JEDG3XR6L6C43KKFCXQ3PHS","short_pith_number":"pith:NS3JEDG3","schema_version":"1.0","canonical_sha256":"6cb6920cdbbc7cbf0b9b528a2bc36f3cbad4ca4f4b830195d23f9090d979f22a","source":{"kind":"arxiv","id":"1309.6767","version":1},"attestation_state":"computed","paper":{"title":"Simultaneous Integer Values of Pairs of Quadratic Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"D. R. Heath-Brown, L. B. Pierce","submitted_at":"2013-09-26T09:22:25Z","abstract_excerpt":"We prove that a pair of integral quadratic forms in 5 or more variables will simultaneously represent \"almost all\" pairs of integers that satisfy the necessary local conditions, provided that the forms satisfy a suitable nonsingularity condition. In particular such forms simultaneously attain prime values if the obvious local conditions hold. The proof uses the circle method, and in particular pioneers a two-dimensional version of a Kloosterman refinement."},"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":"1309.6767","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-26T09:22:25Z","cross_cats_sorted":[],"title_canon_sha256":"f14c911cdaee5278019b13fb64770f90b1bae6878684d35fb2ecafc646fe97db","abstract_canon_sha256":"5b25292dd45d81a021d6788278b8e2a236ba39e116052efdbc38e33678b0eded"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:10.595008Z","signature_b64":"3OMi2UoFVU9LLTQrYoKs0G4z25jLxE1+j2wFpYM8PFtr6ir+Wjb3DHeGTdNIpicOQnU4EZYZXHYfRbOdtYsMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cb6920cdbbc7cbf0b9b528a2bc36f3cbad4ca4f4b830195d23f9090d979f22a","last_reissued_at":"2026-05-18T03:12:10.594123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:10.594123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simultaneous Integer Values of Pairs of Quadratic Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"D. R. Heath-Brown, L. B. Pierce","submitted_at":"2013-09-26T09:22:25Z","abstract_excerpt":"We prove that a pair of integral quadratic forms in 5 or more variables will simultaneously represent \"almost all\" pairs of integers that satisfy the necessary local conditions, provided that the forms satisfy a suitable nonsingularity condition. In particular such forms simultaneously attain prime values if the obvious local conditions hold. The proof uses the circle method, and in particular pioneers a two-dimensional version of a Kloosterman refinement."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6767","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":"1309.6767","created_at":"2026-05-18T03:12:10.594266+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.6767v1","created_at":"2026-05-18T03:12:10.594266+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6767","created_at":"2026-05-18T03:12:10.594266+00:00"},{"alias_kind":"pith_short_12","alias_value":"NS3JEDG3XR6L","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"NS3JEDG3XR6L6C43","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"NS3JEDG3","created_at":"2026-05-18T12:27:52.871228+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/NS3JEDG3XR6L6C43KKFCXQ3PHS","json":"https://pith.science/pith/NS3JEDG3XR6L6C43KKFCXQ3PHS.json","graph_json":"https://pith.science/api/pith-number/NS3JEDG3XR6L6C43KKFCXQ3PHS/graph.json","events_json":"https://pith.science/api/pith-number/NS3JEDG3XR6L6C43KKFCXQ3PHS/events.json","paper":"https://pith.science/paper/NS3JEDG3"},"agent_actions":{"view_html":"https://pith.science/pith/NS3JEDG3XR6L6C43KKFCXQ3PHS","download_json":"https://pith.science/pith/NS3JEDG3XR6L6C43KKFCXQ3PHS.json","view_paper":"https://pith.science/paper/NS3JEDG3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.6767&json=true","fetch_graph":"https://pith.science/api/pith-number/NS3JEDG3XR6L6C43KKFCXQ3PHS/graph.json","fetch_events":"https://pith.science/api/pith-number/NS3JEDG3XR6L6C43KKFCXQ3PHS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NS3JEDG3XR6L6C43KKFCXQ3PHS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NS3JEDG3XR6L6C43KKFCXQ3PHS/action/storage_attestation","attest_author":"https://pith.science/pith/NS3JEDG3XR6L6C43KKFCXQ3PHS/action/author_attestation","sign_citation":"https://pith.science/pith/NS3JEDG3XR6L6C43KKFCXQ3PHS/action/citation_signature","submit_replication":"https://pith.science/pith/NS3JEDG3XR6L6C43KKFCXQ3PHS/action/replication_record"}},"created_at":"2026-05-18T03:12:10.594266+00:00","updated_at":"2026-05-18T03:12:10.594266+00:00"}