{"paper":{"title":"The minimal obstruction modulus for quadratic forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Naoki Ochi","submitted_at":"2026-08-10T03:11:33Z","abstract_excerpt":"Let $Q = ax^2+bxy+cy^2$ be a primitive positive definite integral binary quadratic form with discriminant $\\Delta = b^2-4ac$. It is known that $Q$ admits a local obstruction; that is, there exist $k,l \\in \\mathbb{Z}$ such that $Q \\not\\equiv l \\pmod k$. We study the minimal obstruction modulus $\\kappa_Q := \\min \\{k \\in \\mathbb{Z}_{\\geq 1} \\mid \\text{there exists } l \\text{ such that } Q \\not\\equiv l \\pmod k \\}$, and we determine $\\kappa_Q$ completely, treating the cases $\\Delta \\equiv 0 \\pmod 4$ and $\\Delta \\equiv 1 \\pmod 4$ separately. We also determine the analogous invariants for primitive t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09063","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.09063/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"}