This paper develops a local scaling framework for measurement cost near structural walls in reduced inverse problems. It separates finite walls, governed by a vanishing exponent β, from asymptotic walls, governed by γ, and derives the corresponding cost laws for finite-distance resolution and horizon push-out. The framework is applied to reduced reheating reconstruction and dynamical-decoupling spectroscopy. Fold diagnostics, cusp root scaling with singular-mode lift order, and DD fragility exponents are organized as instances of a common sensitivity-vanishing principle.
Hiroyuki Shioiri (2026) studied this question.