The Witness Gram (Paper III)
Kron-Reduced Laplacian of Hidden Convention Risk
Witness Gram is a Kron-reduced Laplacian; leverage matches exactly across all 240 nonzero-fee cases, including 37 natural partial-CHP regime breaks
A composition where the witness Gram rank disagrees with the coherence fee, or where leverage deviates from (|H_C|−1)/|H_C| per component
Abstract
The witness Gram K(G) = Hᵀ(I − P_O)H of a tool composition is always a Kron-reduced graph Laplacian. Under Dimension-Field Disjointness it decomposes as a direct sum of per-dimension carrier-graph Laplacians; without DFD it remains a single Kron-reduced Laplacian of the merged coboundary-incidence graph. Effective resistance between hidden fields quantifies disclosure substitutability: the smaller the resistance, the more equivalent the fields are as repair choices.