General Theory of Finite Obstruction Calculus

This document presents the General Theory of Finite Obstruction Calculus, a finite mathematical framework for evaluating defects, repairs, residual classes, and licensed representational lifts in contextual symbolic systems. A finite obstruction level consists of finite term and context categories, a context action, a finite cochain complex C^0 -> C^1 -> C^2, a declared gauge, and a quotient profile map. Exact repairs are represented by im(d_0), quotient obstruction by Q^1 = C^1 / im(d_0), and closed non-exact residue by H^1 = ker(dbar_1), where dbar_1 is the induced map on the quotient. The framework includes weighted obstruction norms, primal-dual certificates, observer quotients, context-witness lift triggers, minimal resolver conditions, skeleton preservation, and no-silent-mutation laws. This calculus is intended as the finite obstruction engine used by Finite Descent Authority, not as an independent source of authority. It provides the algebraic and cohomological underpinnings for the layer factorization and no-shortcut theorem of finite sound authority systems.