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It is called complete if it is of the form $Q({\\mathbf x} + {\\mathbf v})$, where $Q$ is an integral quadratic form in the variables ${\\mathbf x} = (x_1, \\ldots, x_n)$ and ${\\mathbf v}$ is a vector in ${\\mathbb Q}^n$. Its conductor is defined to be the smallest positive integer $c$ such that $c{\\mathbf v} \\in {\\mathbb Z}^n$. We prove that for a fixed positive integer $c$, there are only finitely many equ"},"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":"1505.00281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-01T20:49:36Z","cross_cats_sorted":[],"title_canon_sha256":"0385935ac09380c90f8c1736a0d46cfcffc067cf19712886732eb2b643a2e9ab","abstract_canon_sha256":"7714f742626435bb5699b1fc0c1551526227ca7512626fefdc4388bf1c4c4d65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:10.588492Z","signature_b64":"OVghzmSfT+7TjGRoSsszySGQyK88/9DaxJ9RYq4uRqoRlu+kjAOSymoZp37HC8ZJKBi04TfakT25uY8dQfp3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"387eb8cbb59c33307aafd164b20fb8d8805c2c742bba4d04710fc2d69998e1ea","last_reissued_at":"2026-05-18T02:17:10.587912Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:10.587912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The representation of integers by positive ternary quadratic polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"James Ricci, Wai Kiu Chan","submitted_at":"2015-05-01T20:49:36Z","abstract_excerpt":"An integral quadratic polynomial is called regular if it represents every integer that is represented by the polynomial itself over the reals and over the $p$-adic integers for every prime $p$. 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