Sectoral Selection Rules from Toroidal QDC Closure: Family Characters, Koide-Phase Reconstruction, Vacuum Projection, BSM Exclusion, and Testable Recurrence Thresholds in the Quantized Dimensional Ledger

This work develops conditional sectoral selection rules from the toroidal Quantized Dimensional Cell (QDC) closure construction within the Quantized Dimensional Ledger (QDL) program. The toroidal QDC closure cell represents the QDL persistence cell L³F² as a compact recurrence geometry with effective spatial occupancy and two independent recurrence frequencies. The paper studies six sectoral projections of the toroidal QDC closure-stable residue: family structure, charged-lepton mass-ratio reconstruction, vacuum residual selection, gauge-sector closure, beyond-Standard-Model admissibility and exclusion, and QDC-linked recurrence thresholds. It formulates a primitive recurrence-character family-count theorem under stated QDL assumptions, a fixed toroidal phase rule for Koide-phase charged-lepton mass-ratio reconstruction, a closure-projected vacuum residual model, a compensator-complete gauge and BSM exclusion rule, and a reduced Compton–gravity recurrence threshold tied to the QDC. The work does not claim an unconditional derivation of the Standard Model, a final theory of quantum gravity, a numerical solution of the cosmological constant problem, or a universal exclusion of all beyond-Standard-Model physics. Instead, it presents a conditional sectoral selection framework whose outputs are explicitly claim-governed and falsifiable through identifiable failure modes.