{"paper":{"title":"Symmetric $\\epsilon$- and $(\\epsilon+1/2)$-forms and quadratic constraints in \"elliptic\" sectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Roman N. Lee","submitted_at":"2018-06-13T04:59:50Z","abstract_excerpt":"Within the differential equation method for multiloop calculations, we examine the systems irreducible to $\\epsilon$-form. We argue that for many cases of such systems it is possible to obtain nontrivial quadratic constraints on the coefficients of $\\epsilon$-expansion of their homogeneous solutions. These constraints are the direct consequence of the existence of symmetric $(\\epsilon+1/2)$-form of the homogeneous differential system, i.e., the form where the matrix in the right-hand side is symmetric and its $\\epsilon$-dependence is localized in the overall factor $(\\epsilon+1/2)$. The existe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04846","kind":"arxiv","version":2},"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"}