Toroidal Closure-Cell Geometry for Planck-Normalized Dimensional Recurrence in the Quantized Dimensional Ledger

This preprint develops a toroidal closure-cell representation of the Quantized Dimensional Ledger persistence signature L³F². The construction interprets L³ as effective spatial occupancy and F² as two-cycle recurrence, represented by a compact toroidal recurrence candidate T₍, ₌ with winding data, sectoral data, effective occupancy volume, and recurrence frequencies. A toroidal QDC measure QDCT = VT omega₁ omega₂ is introduced, and physical persistence is defined by survival under a toroidal QDL closure functional. The paper emphasizes that the toroidal closure cell is not a material aether, classical medium, or claim that physical space contains literal toroidal objects. It is a closure-space representation of Planck-normalized dimensional recurrence. The work includes Planck-normalized anchors such as GM having dimensional form L³F², the Planck identity GMP = LP³ FP², and the reduced Compton-gravity threshold m_* = mP / sqrt (2). To connect the construction with established theoretical physics, the paper applies the closure-vector method to a representative Standard Model Effective Field Theory audit. Dimension-six Warsaw-basis operator classes are assigned reduced closure vectors, and selected anomalous-dimension structures are classified as closure-preserving, closure-compensated, or residual-forcing. The SMEFT section is not a completed full anomalous-dimension matrix audit; it is a reproducible criterion for testing whether known nonzero operator-mixing entries preserve declared closure vectors or require explicit Standard Model compensators. The paper is part of the QDL closure-admissibility program and is intended as a full archival version for Zenodo. Conditional extensions to particle-sector classification, vacuum filtering, mass-spectrum projections, and quantum-geometric state selection are identified as future tests rather than established results.