The Ratio of Equations by Vineet Kumar 'V.2.0': The Geometric and Algebraic Properties of Inconsistent Systems:
Vineet Kumar Prasad · 2026
An analytical formalization of the algebraic and geometric boundary properties governing inconsistent linear frameworks. This paper introduces and proves the 'Ratio of Equations by Vineet Kumar', establishing that the coordinate axis variance from a system vertex to an non-intersecting linear boundary forms an absolute invariant determined strictly by the boundary's linear coefficients. Includes structural classifications, analytical derivations, numerical system examples, and localized verification scripts.