A Residual--Excess Framework for Defect Resolutions: Finite-Node Saito Gluing and Integral Hodge Obstructions

Defect data attached to a morphism admit two orthogonal refinements. The first is factorization-sensitive: a factorization \(A{u}B{v}A^\), with \(vu=R\), gives a residual triple \((Cone(u),Cone(v),Cone(R))\) constrained by the octahedral axiom. The second is coefficient-sensitive: an excess object is the cone of a comparison morphism between integral or finite-coefficient residual data and its rational or mixed-Hodge realization. We organize these two directions into a residual--excess matrix. The main residual witness is a finite ordinary-double-point conifold degeneration. Saito divisor gluing produces a node-supported Hodge interface \(W^H_Σ=p_k∈Σik* Q^H_{\{p_k\}}(-1)\), factoring finite-node monodromy through \(ψ^Hπ,1→ W^H_Σ→ψ^Hπ,1(-1)\). The variation cone yields the corrected extension \(0→ IC^HX_0→ P^Hvar,Σ→ W^H_Σ→0\), whose class decomposes into nodewise Ext residual classes. Ordinary double points calibrate the zero-excess regime because their Milnor fibers are integrally torsion-free. Diaz's Enriques-product Bockstein mechanism calibrates the nonzero-excess regime through integral torsion killed by rationalization. The resulting framework compares finite-node Saito gluing with integral Hodge obstruction channels without conflating rational residual data with coefficient-change defects.