A Pre-Geometric Causal Invariant: A Green–Kubo Closure for the Light Cone and the Arrow of Time.

This preprint develops a conditional mathematical mechanism for the emergence of a protected causal cone within the Theory of Structural Articulation. The central object is not the full spectrum of the microscopic generator, but the current-cyclic spectral measure visible to the Green-Kubo response of a protected current channel. The paper proves that, under three explicit conditions — the existence of a protected passive current channel, a low-frequency current-cyclic rank-one closure, and a Ward-type long-wavelength density-current coupling — the protected causal speed is fixed by the product of an articulational Green-Kubo transport capacity and a protected relaxation edge. This gives a precise route from a pregeometric current response to a Maxwell-Cattaneo-type hyperbolic principal symbol. A key feature of the construction is the separation between the protected causal ceiling and its observable electromagnetic readout. The paper does not assume that the observed speed of light is obtained unconditionally. Instead, equality with the observed electromagnetic cone is treated as a separate readout-saturation condition requiring an unbroken massless U(1) branch and absence of loss in the transverse time-even readout channel. The article also introduces finite-dimensional verification criteria for the protected sector, including charge-conservation checks via the kernel of the local-move matrix, current-cyclic spectral measures, pole-defect diagnostics, low-frequency causal closure rank, and explicit finite carrier models. Chain-complex and parity-based examples show that the class of protected carriers satisfying the required assumptions is non-empty. The work further clarifies the relationship between Green-Kubo transport, Mori-Zwanzig reduction, Maxwell-Cattaneo closure, the protected causal cone, and the asymptotic arrow of time. The result is formulated as a conditional theorem in mathematical physics: it establishes a protected causal invariant inside a specified class of pregeometric current channels, while keeping SI calibration and electromagnetic readout as separate additional layers.