Asymptotic-Safety Truncations as Conditional Shadows: Fixed-Point Residuals, Error Bounds, and Scheme Dependence

Finite functional-renormalization-group truncations can reveal fixed-point structure, but a truncation fixed point is not automatically the shadow of an exact ultraviolet completion. This paper gives a validation framework for that inference. A contraction residual bounds the distance to an exact fixed point when the exact map is already known to be contractive. A finite truncation has its own fixed point only when an independent existence condition, such as invariant contraction or a verified degree argument, is supplied. If a lifted truncation fixed point has a certified defect relative to the exact map, its distance from the exact fixed point is bounded by that defect divided by the contraction margin. An additive-error Lipschitz inequality alone proves none of these conclusions. Applied to Modal Triplet Theory, the framework identifies the missing data: a selected map from coherent variables to FRG couplings, a physical regulator and scheme, and certified truncation defects. The paper therefore supplies a rigorous truncation diagnostic, not a proof that current asymptotic-safety truncations are MTT predictions.