The G6 Crystal: A dm3-Derived Architectural Form for Resonance-Stable Tall Structures

We present a structural geometry — the G6 Crystal — derived from first principles via the dm3 generative contact mechanics framework. The geometry is fully determined by three canonical invariants: period T* = 2π, maximal transverse Lyapunov exponent μ_max = −2, and embodiment threshold τ = 2. Six applications of the operator G = U∘F∘K∘C produce a hexagonal tower with total height 33,000 cubits = 15,087.6 m and aspect ratio 66 = 33·τ. Three independent results are established: hexagonal isoperimetric optimum (15.47% improvement over square), hexagrid structural efficiency verified against peer-reviewed literature, and passive Schumann n=4 resonance coupling at 33.516 Hz via Arnold tongue A4:1 with noise tolerance τ·ε₀ = 2/3.