Planck-Scale Toroidal Closure Substrate: Dimensional Recurrence, Structural Admissibility, and Theory Appraisal in the Quantized Dimensional Ledger

This paper develops a foundations-level interpretation of the Quantized Dimensional Ledger (QDL) as a structural-admissibility framework for physical theory construction. It identifies the recurring dimensional cell L3F2L^{3}F^{2}L3F2 in gravitational, orbital, and Planck-normalized reconstruction, formalizes the associated typed toroidal Quantized Dimensional Cell TQDC5=(SL1)3×(SF1)2T^{5}_{QDC}=(S^{1}_{L})^{3}\times(S^{1}_{F})^{2}TQDC5=(SL1)3×(SF1)2, and interprets the resulting structure as a Planck-scale toroidal closure substrate. The paper distinguishes this substrate from classical aether concepts, situates QDL within debates about dimensional analysis, scientific representation, structural realism, theory appraisal, and measurement, and defines claim-status boundaries between established dimensional facts, QDL definitions, conditional results, interpretive claims, and open conjectures. It also includes a worked μ\muμ-ledger example showing how closure-admissibility can be operationalized through orbital residual analysis.