Geometry of the G Model: From Cube to Four-Null Tetrahedron

The cube was the natural engineering starting point because it is easy to draw, repeat, and connect, but it was not retained as the primitive physical cell because its explicit axes, multiple primitive distance classes, and higher-order anisotropy preserve directional structure.

Four equal tetrahedral directions are the first balanced, genuinely non-planar set in three spatial dimensions. They have zero vector sum, equal pair dot products of -1/3, tetrahedral angle approximately 109.47 degrees, and an isotropic quadratic moment.

Promoting those directions to four future-directed null branches produces six pairwise bivector channels. The four-null Gram matrix has Lorentzian signature, is non-degenerate, and reconstructs Minkowski geometry within the stated local construction.

The geometry fixes several exact ratios and decompositions, while the native causal volume remains a model definition and the retained CΣ coefficient also uses response and averaging choices whose physical uniqueness is not yet proved.

The six tetrahedral edge midpoints supply a natural six-port connection architecture. The cube remains useful only as an auxiliary construction box, not as the retained physical local module.

These exact labels apply inside the declared mathematical construction. They do not establish all-scale Lorentz invariance, microscopic dynamics, an absolute numerical time scale, or experimental reality.