Spin-2 Obstruction and Conditional Metric Dynamics in a Weighted QDC Contact Frame: Coframe Hessian, Torsion-Loop Extension, Constraint Algebra, Extra-Mode Decoupling, and Dispersive Residuals

This record contains the main preprint and its accompanying Technical Supplement. The study examines whether a weighted two-shell body-centered-cubic contact frame motivated by the Quantized Dimensional Cell can generate an autonomous massless spin-2 gravitational sector. Its principal result is an exact obstruction within a precisely specified microscopic model. When all sixteen coframe components receive positive componentwise inertia and the same weighted-BCC bond operator, the velocity Hessian is positive and full rank. The Legendre map is therefore invertible, no Hessian-generated primary constraints arise, and all sixteen frame components propagate. Fourth-order contact isotropy and a shared relativistic-looking characteristic cone are consequently insufficient to produce a constrained two-degree-of-freedom massless spin-2 theory. A second construction is developed under an additional integrable-frame null-energy hypothesis that is not derived from QDL closure. This hypothesis replaces ordinary componentwise frame-gradient energy with an antisymmetrized coframe derivative or torsion. The resulting discrete torsion-loop construction has the parity-even quadratic teleparallel or new-general-relativity class as its leading continuum limit. Weighted-BCC isotropy fixes the derivative geometry but does not determine the three independent torsion-contraction coefficients. The Einstein-equivalent branch therefore additionally requires the TEGR coefficient ratio, local Lorentz redundancy, absence of algebraic metric strain, suppression of preferred-frame operators, positive tensor normalization, matter-compatible constraints, and infrared closure of the discrete constraint algebra. For the specific tensor and matter lattice operators tested, the sectors share a leading cone but have different first dispersive corrections, producing the operator-pair residual Delta_Tm^(4) = -1/8. This value is not claimed as a universal QDC constant. The Technical Supplement provides the complete contact-moment, lattice-symbol, Hamiltonian, centered-derivative, sixth-order anisotropy, tensor-variation, transverse-traceless projector, degree-of-freedom, TEGR-diagnostic, preferred-frame, time-delay, and continuum-versus-discrete constraint-algebra derivations. The record establishes a rigorous obstruction to the minimal componentwise QDC frame and a finite conditional route to an Einstein-equivalent torsion branch. It does not claim an unconditional microscopic derivation of general relativity, Newton’s constant, the exact discrete gravitational constraint algebra, quantum gravity, or the cosmological constant.