A Clifford-Encoding Model for Lorentzian Metrics in Entropic Gravity Frameworks

A positive control metric cannot become Lorentzian by a change of variables. We instead derive the relative sign from the propagation of an internal quantum state. For a first-order Hermitian symbol with linearly independent spatial coefficients, every band lies on one quadratic shell if and only if the coefficients obey the corresponding Euclidean Clifford relations. Operator-norm bounds on deviations give a uniform squared-band certificate without asserting repair to an exact representation. The resulting form $\omega^2-Q(q)$ has signature $(1,d)$; it describes the full characteristic cone when both frequency branches occur. The evolution parameter is supplied, while unitarity makes its conjugate frequency a hyperbolicity direction. The internal dimension bounds $d+[\mu\neq0]$ by $2\nu_2(s)+1$, so a qubit supports a massless shell in at most three spatial dimensions. On a lattice, the strict support cone, maximum group speed and low-energy read-out cone differ. For several species, off-diagonal mixing with fixed diagonal principal blocks cannot produce a single quadratic shell. Interactions can align speeds: in a one-loop mediator model, divergent accumulated coupling along every edge is sufficient, even when their active ranges of renormalization scale are disjoint. Near a supplied Lorentz-invariant conformal fixed point, additional conserved spin-2 currents mark the marginal exceptions to speed alignment. A finite record protocol for the same coined walk certifies its mass-setting angle, separating the ideal rest-and-curvature and group speeds from each other and from the supplied support speed. The geometric dictionary, actual noisy transport and physical inputs remain separate.