CF01: Complete Formalism - Quantum Geometric Tensor to Metriplectic Brackets

We construct a complete formalism mapping the quantum geometric tensor (QGT) of asmooth eigenbundle to a candidate metriplectic split in the Void Dynamics Model (VDM)sense. The antisymmetric part of the QGT (Berry curvature) defines a closed two-formthat induces a Poisson bracket on any symplectic leaf where the curvature has full rank,yielding a Hamiltonian generator J. The symmetric part (quantum metric) induces a positivesemidefinite metric bracket; we give an explicit projection construction producing a degeneratemetric operator M that preserves a chosen invariant functional I while monotonicallyincreasing an entropy-like functional Σ, matching the VDM degeneracy constraints. Thepaper specifies decisive falsifiers (gauge invariance, Jacobi residual, positive-semidefiniteness,and degeneracy residuals), provides a constructive algorithm for computing g, Ω, J, and Mfrom numerical eigenstates, and works an analytic two-level example.