OG-II-05 — U — A Conforming Aperiodic Regulator for Linearized Vacuum Gravity - A conforming divdiv complex, exact constraints, and Fibonacci time

We construct a conforming tensor-field regulator for linearized vacuum gravity on a specified complete aperiodic D₆/H₃ carrier. Physical Delaunay cells and their canonical barycentric tetrahedralization give a uniformly controlled mesh. A fixed Chen–Huang divdiv complex with degrees (k+2,k+1,k,k−2), k≥3, defines a completed Hodge–Dirac evolution with exact energy conservation and an invariant constraint sector. Canonical interpolation preserves the terminal divdiv constraint. Orthogonal L² projection at the scalar endpoint cancels the terminal adjoint residual exactly. The resulting spatial error is O(hᵏ⁻¹) for the smooth completed system and O(hᵏ) on the exactly initialized smooth constraint sector. In particular, k=4 gives a proved O(h⁴) constrained spatial bound, and k=3 is admissible. Variable-step midpoint preserves energy and constraints and has O(hᵏ+δmax²) constrained error under the stated regularity assumptions, without a CFL restriction. Density extends compact-time strong convergence to all well-prepared constrained finite-energy data. An explicit spacetime reconstruction separates transverse-traceless amplitudes from coordinate modes in the constrained variables. A linearized diffeomorphism removes the coordinate part, leaving a vacuum Einstein wave with exactly two nonzero-momentum physical polarizations. Local algebraic calculations support the polynomial and symbol identities; the complete-carrier estimates are proved analytically. The tensor variables, positive energy, Lorentzian background and time calibration are declared dynamical inputs.