Abstract

This note assembles a conditional Lorentz-cone representation theorem and a separate operational approximation corollary on a named tripartite qubit process-matrix interface. The theorem assumes a predeclared nonempty admissible domain, a single-valued faithful generated affine representation rule, its matched covariance, and homogeneity and cone strict convexity. Published classification then gives a Lorentz cone and a conformal quadratic form. The implication is proved; no operational package satisfying all its hypotheses is constructed. A further symmetry obstruction shows that infinitely repeated indistinguishable experiment blocks cannot admit an injective finite-dimensional embedding covariant under every matched permutation. Conditional on supplied compatible transport protocols, complete-channel telescoping yields endpoint, reference, residual, and arrival-window bounds. Execution resources, classical extraction costs, estimation shots, and retained outputs are separated. An optional finite full-output validation certificate is proved under explicit sampling and calibration assumptions. Finite generation, finite futures, nonzero tolerances, and dynamics limitations remain visible. The release is a self-contained conditional assembly and audit, not an existence theorem for operational spacetime emergence, a metric-field construction, or Einstein dynamics.