{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:Q6RELNWXACY3CU7O3RXO3SQEUL","short_pith_number":"pith:Q6RELNWX","schema_version":"1.0","canonical_sha256":"87a245b6d700b1b153eedc6eedca04a2deaea463a99c7b7f7de9585ad010daed","source":{"kind":"arxiv","id":"1112.2991","version":1},"attestation_state":"computed","paper":{"title":"Strong approximation for the total space of certain quadric fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Fei Xu, Jean-Louis Colliot-Th\\'el\\`ene","submitted_at":"2011-12-13T18:19:14Z","abstract_excerpt":"We study equations in four variables (x,y,z,t) of the shape q(x,y,z)=P(t), where q(x,y,z) is an indefinite ternary quadratic form over the integers and P(t) is a polynomial in one variable with integral coefficients. If P(t) is not the product of a constant and the square of a polynomial, strong approximation holds for integral solutions (x,y,z,t). In the general case, we show that the integral Brauer-Manin conditions are the only obstructions to strong approximation. We actually study the analogous situation over an arbitrary number field.\n  ---\n  Nous \\'etudions les \\'equations \\`a quatre va"},"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":"1112.2991","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-13T18:19:14Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"fefb43ccf1bfcbba3b5fa89381c4415b40bfe40af6afdddbbd92dfa91eee2f97","abstract_canon_sha256":"b277b4acbd7197f8c8d51ef41901263c95c591962ba60ec05743805c5dbd4faf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:31.841466Z","signature_b64":"pepGtpMllU01i0On3cR0lvKUXwPZMrDBan0Y9hAdCeU/YzkAZa15lCK83oIU3ocLjooTXyw/9GCUf5H0J/3fDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87a245b6d700b1b153eedc6eedca04a2deaea463a99c7b7f7de9585ad010daed","last_reissued_at":"2026-05-18T04:06:31.840835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:31.840835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong approximation for the total space of certain quadric fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Fei Xu, Jean-Louis Colliot-Th\\'el\\`ene","submitted_at":"2011-12-13T18:19:14Z","abstract_excerpt":"We study equations in four variables (x,y,z,t) of the shape q(x,y,z)=P(t), where q(x,y,z) is an indefinite ternary quadratic form over the integers and P(t) is a polynomial in one variable with integral coefficients. If P(t) is not the product of a constant and the square of a polynomial, strong approximation holds for integral solutions (x,y,z,t). In the general case, we show that the integral Brauer-Manin conditions are the only obstructions to strong approximation. We actually study the analogous situation over an arbitrary number field.\n  ---\n  Nous \\'etudions les \\'equations \\`a quatre va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2991","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":"1112.2991","created_at":"2026-05-18T04:06:31.840941+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.2991v1","created_at":"2026-05-18T04:06:31.840941+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2991","created_at":"2026-05-18T04:06:31.840941+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q6RELNWXACY3","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q6RELNWXACY3CU7O","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q6RELNWX","created_at":"2026-05-18T12:26:39.201973+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/Q6RELNWXACY3CU7O3RXO3SQEUL","json":"https://pith.science/pith/Q6RELNWXACY3CU7O3RXO3SQEUL.json","graph_json":"https://pith.science/api/pith-number/Q6RELNWXACY3CU7O3RXO3SQEUL/graph.json","events_json":"https://pith.science/api/pith-number/Q6RELNWXACY3CU7O3RXO3SQEUL/events.json","paper":"https://pith.science/paper/Q6RELNWX"},"agent_actions":{"view_html":"https://pith.science/pith/Q6RELNWXACY3CU7O3RXO3SQEUL","download_json":"https://pith.science/pith/Q6RELNWXACY3CU7O3RXO3SQEUL.json","view_paper":"https://pith.science/paper/Q6RELNWX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.2991&json=true","fetch_graph":"https://pith.science/api/pith-number/Q6RELNWXACY3CU7O3RXO3SQEUL/graph.json","fetch_events":"https://pith.science/api/pith-number/Q6RELNWXACY3CU7O3RXO3SQEUL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q6RELNWXACY3CU7O3RXO3SQEUL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q6RELNWXACY3CU7O3RXO3SQEUL/action/storage_attestation","attest_author":"https://pith.science/pith/Q6RELNWXACY3CU7O3RXO3SQEUL/action/author_attestation","sign_citation":"https://pith.science/pith/Q6RELNWXACY3CU7O3RXO3SQEUL/action/citation_signature","submit_replication":"https://pith.science/pith/Q6RELNWXACY3CU7O3RXO3SQEUL/action/replication_record"}},"created_at":"2026-05-18T04:06:31.840941+00:00","updated_at":"2026-05-18T04:06:31.840941+00:00"}