Solver-Agnostic Convergence Certificates for DSGE Computation in Economics

We propose a solver-agnostic framework for analysing convergence in DSGE computation based on a single quadratic \emph{residual of sameness} measured in a fixed, calibrated norm. In the Deterministic Statistical Feedback Law (DSFL) view, an economic model is specified by a frozen defect representation and a declared symmetric positive definite ruler that aggregates equilibrium violations. Once this geometry is fixed, solver behaviour becomes a typed statement about the induced defect dynamics rather than an implementation-dependent notion of error. We show that standard DSGE solvers—time iteration, policy iteration, and Newton or quasi-Newton methods—can be analysed as residual-updating maps whose contraction properties yield explicit convergence envelopes, robust stopping rules under numerical forcing, and comparable rate diagnostics. A Gram-operator construction provides a single solver-agnostic contraction score and exposes non-normal transient amplification that eigenvalue diagnostics alone can miss. Numerical studies for a small New Keynesian model illustrate how the framework enables reproducible and interpretable solver comparisons within a single geometric language.