Corner-cofactor descent for skew Schur compositions

We prove an exact formula for the extreme Jacobi–Trudi cofactor of a marked skew composition under Hypotheses I–IV of McNamara and van Willigenburg, without Hypothesis V, using Olson-Harris's composition homomorphism. The formula separates the compositions of the outer diagram's interior components from normalization factors whose largest complete-function indices are smaller than the composition period. Irreducible factorization consequently identifies every transported interior component above this threshold, with multiplicity. Combined with common-divisor gluing for two charts of one diagram, this gives a descent for comparing source-minimal periods of Schur-equal diagrams: a least-span failure has only isolated cells in the larger-period outer's southeast interior. The cofactor also gives congruence and multiplicity obstructions to proposed periods. An explicit unbounded family outside Hypothesis V shows that the composition proof of McNamara and van Willigenburg genuinely uses that hypothesis. The discrete-interior comparison remains open.