A Conditional Light-Cone Interface of a Four-Dimensional Lorentzian Matter Phase in an SL(6,C)-Motivated Reduction

We study the causal meaning of a light-speed interface for a four-dimensional Lorentzian matter sector in an \( SL(6,\mathbb C) \)-motivated six-dimensional program. We separate Gaussian statistical localization, physical signature selection, projectable geometric reduction, and low-energy truncation. Positive precision cannot generate a timelike direction, and unimodular complex congruence obstructs a single-sign-flip real endpoint. On a supplied regular six-dimensional Lorentzian branch with positive internal fibers, the quotient is Lorentzian and causal projection yields a sharp local speed bound. We derive a finite-window criterion in which an internal gap and a positive four-dimensional Planck coefficient coexist; unlimited localization does not preserve that window. A common regular scalar principal symbol then identifies the quotient metric cone. The light-speed interface is consequently a causal boundary within the controlled four-dimensional phase, while access to internal modes is set by an energy threshold rather than a velocity test. The fast–slow exponential model, entropy and symmetry mechanisms, and observable diagnostics are retained with separate clocks and matching assumptions.