Conformal information is not dynamics

A full affine Lorentz cone determines $[q_D]$, not a preferred observer, physical normalization, or system of units. If

its normalized null slope becomes ${\ell }_0/{\tau }_0$. Those calibration constants are not selected by cone membership CheungXXIID (prop:calibration).

Translating a constant representative across its affine carrier gives constant metric components. Its Christoffel symbols and curvature are zero. Even after a local differentiable extension is supplied, positive conformal multiplication preserves every pointwise cone. With signature $(+,-,\dots ,-)$, the first variation of $e^{2\lambda f}\eta$ is $2f\eta$, and

The right side can be nonzero while all cone fields are unchanged. XXII-E supplies this calculation and its precise comparator conventions CheungXXIIE (thm:flat, prop:conformal).

Neither a process matrix nor an identity transport channel assigns a matter Hamiltonian or stress-energy tensor. Symmetry and conservation alone also allow nonzero improvements of the displayed derivative form CheungXXIIE (prop:energy, prop:improvement). Consequently, no dynamics matching is hidden in Theorem thm:assembly or its approximation corollary.