Lorentzian Signature as Algebraic Causality in FRC

We show that a genuine Lorentzian quadratic form on a prime shell cannot be realized within a single symmetry-complete finite field \(\mathbb F_{\mathsf p}\). The obstruction is elementary: to split time from space one needs a time coefficient \(c^2\) in the nonsquare class of \(\mathbb F_{\mathsf p}^{\times}\), but then \(c \notin \mathbb F_{\mathsf p}\). Thus, the minimal construction of a Minkowski metric in the Finite Ring Continuum (FRC) requires the quadratic extension \(\mathbb F_{\mathsf{p}^2}\) (``the next shell''), where such a \(c\) exists. We interpret this obstruction as the algebraic origin of causal structure: just as the South Pole of the orbital complex \(\mathcal S_{\mathsf p}\) lies beyond an observer's horizon, the constant distinguishing time from space lies beyond the local field. Causality, in this sense, is encoded as algebraic inaccessibility, becoming available only by extension beyond the shell. This short note isolates the mechanism in a minimal form, making the causal significance of square-class separation explicit and fully reproducible.