Structural Admissibility and Scientific Representation: From Operator Filtering to Representation Governance in the Quantized Dimensional Ledger

This paper develops structural admissibility as a constraint on scientific representation and uses the Quantized Dimensional Ledger (QDL) as a formal framework for articulating that constraint. Scientific representations are commonly evaluated by empirical adequacy, mathematical consistency, explanatory utility, robustness, and pragmatic usefulness. Dimensional homogeneity supplies an additional requirement, but the paper argues that dimensional homogeneity alone is not sufficient for representational legitimacy when models are transformed, truncated, calibrated, coupled, simulated, coarse-grained, or embedded in measurement chains.

The central claim is that admissibility should not be understood only as a filter on static objects. If scientific representations are used through transformations, then admissibility must also govern the maps by which one representation is carried into another. The paper introduces the concept of an admissibility-preserving map and develops a minimal formal scaffold consisting of ledger space, ledger map, admissibility operator, admissible kernel, induced representation maps, closure-equivalence, and admissibility preservation.

The main formal result proves that, for induced linear maps on ledger space, admissibility preservation is equivalent to invariance of the admissible kernel and to quotient compatibility. A worked toy effective-field-theory truncation example shows how a transformation can preserve ordinary dimensional form while destroying the kernel relation required for structural admissibility.

The paper is not a completed physical theory, a derivation of the Standard Model, or a substitute for empirical testing. Its contribution is methodological and philosophical: structural admissibility is proposed as a prior constraint on scientific representation, and admissibility-preserving maps are identified as the formal object required to extend QDL from operator filtering to representation governance. The paper distinguishes empirical adequacy, dimensional consistency, and structural legitimacy as separate dimensions of model evaluation.