Positivity-Preserving Reduction and Conditional Causal Cones: Geometric Inputs and Effective Limits

We separate a restricted obstruction from conditional effective constructions in a model motivated by SL(6,C). Positive statistical geometry supplies neither a spacetime metric, a time orientation nor a physical light-speed scale. A separately supplied Lorentzian parent can instead yield a four-dimensional quotient with positive internal fibers. We prove semantic closure of the permitted operations and a Schur negative-index equivalence through negative subspaces, while making smoothness and projectability requirements explicit. A specified common-metric action yields metric-null wave characteristics; gauge reduction and the distinction from dust transport are essential. Two wave completions of the same diffusion demonstrate that statistical rates do not select the causal cone. An independent weighted-root model yields a held-out rate relation, calibration degeneracies and an error-controlled rejection criterion. A clock–dust–gravity realization propagates its homogeneous Friedmann constraint, and a compactification dictionary supplies a finite joint energy and gravitational window with uncertainty bounds. An input inventory identifies the assumptions consumed by each result. The accompanying Lean source extends finite algebra, quadratic symbols, constraint ideals and finite Hermite truncations without claiming a full smooth quotient, closed-operator realization or covariant Cauchy theorem. The results delimit a conditional causal theory.