Toroidal QDC Closure and Standard-Model Admissibility: Gauge-Sector Reconstruction, Hypercharge Residues, and Gravitational Closure in the Quantized Dimensional Ledger

This preprint develops a theoretical closure-admissibility architecture within the Quantized Dimensional Ledger (QDL), using a toroidal Quantized Dimensional Cell (QDC) as the primitive substrate. The QDC is represented as a five-dimensional recurrence torus with three length cycles and two frequency cycles. Its closure functional is CQDC (w) = 2 SigmaL - 3 SigmaF, with closure lattice LQDC = ker CQDC. The 3 + 2 QDC split is treated explicitly as a primitive QDL substrate postulate motivated by the gravitational closure cell L³ F², not as a theorem derived from a deeper principle in this paper. Physical sectors are treated as projections of the QDC closure lattice. Under declared admissibility requirements, including closure stability, oriented projection, anomaly-residue cancellation, compensator completeness, primitive residual-orbit minimality, and gravitational L³ F² closure, the paper reconstructs Standard-Model gauge and matter structure as a minimal local closure-stable projection under stated assumptions. Exact anchors include the QDC closure functional, the L³ F² gravitational cell, the Planck gravitational identity G MP = LP³ FP², the Compton-gravity threshold mP / sqrt (2), and, under the declared one-generation Standard Model matter/Higgs basis, the anomaly/Yukawa hypercharge vector (1, -4, 2, -3, 6, 3). The paper separates strict derivations, conditional reconstructions, formal conjectures, structurally constrained sectors, and open completion targets. Gauge-sector reconstruction from QDC stabilizers is conditional on the primitive 3 + 2 substrate postulate and the unitary irreducible projection assumption. The three-generation mechanism is presented as a formal family-orbit conjecture requiring explicit automorphism computation. Masses, coupling constants, mixing matrices, dark matter, and cosmological residual magnitudes are treated as structurally constrained but incomplete completion sectors. The work is not presented as a completed final theory, but as a testable closure architecture for organizing Standard-Model, gravitational, and cosmological admissibility within one quantized dimensional substrate framework.