Internal Two-Parameter Calculus on RIG Path Algebras: Differential Forms, Resonance, and Absolute Extensions

We construct a division-free differential graded algebra for polynomial two-parameter differentiation with arbitrary parameters in a finite RIG path algebra. We characterize generation by functions and their differentials and classify isomorphisms fixing functions and external weights. The cohomology decomposes into finite Koszul blocks. At reflection resonance an explicit contraction removes all blocks with an odd weight and leaves a differential graded algebra near the identity parameter. Finite sampling integrals satisfy Stokes and integration by parts, while polynomial Hasse operators retain Taylor data when ordinary iterated derivatives vanish. An extension to ordinary internal Kähler differentials on the full mixed form module exists precisely when every unit-normalized parameter ratio is internally constant. Its connection correction is explicit and flat. Algebraic constructions retain the original localized integer ring; dimension statements specify real scalar extension.