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Our proof is based on a combination of methods from additive combinatorics due to Green-Tao and Green-Tao-Ziegler, together with an application of the descent theory of Colliot-Th\\'el\\`ene and Sansuc."},"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":"1307.7641","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-29T16:54:03Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"80231862827b10d6cd0f2bdc3365a62fe5e5aab977c664f9f6f881f0aed190aa","abstract_canon_sha256":"875da8cc7165757e5391d09d87ac44879d8cb748b1ce22699717b3e65ac9bfe8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:13.049469Z","signature_b64":"Med0wHvHJn0cBAqx0H17JjImKTmE5XG87Uo7ny02B3smwZyRUWazccD1l2Dfwcn3W7Cq5n7m+GF1f+MQ7a8iCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3540906019a1aeba6f9b41eced9273bf5f6ec3e3147b3c85043838f5b8d1213d","last_reissued_at":"2026-05-18T01:05:13.048690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:13.048690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Norm forms for arbitrary number fields as products of linear polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Lilian Matthiesen, Tim Browning","submitted_at":"2013-07-29T16:54:03Z","abstract_excerpt":"Let K/Q be a field extension of finite degree and let P(t) be a polynomial over Q that splits into linear factors over Q. 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