Invariant Light-Cone Algebra and Emergent Causal Structure

We propose a pre-geometric research programme in which the invariance of the speed of light is not a postulate of spacetime geometry, but rather a consequence of the causal propagation cone encoded in a primitive algebraic structure. Working in natural units (c = 1), the vacuum speed of light is embedded as a central element of an abstract C*-algebra 𝒜, and the light-cone structure emerges from the algebra rather than being assumed a priori. We postulate the existence of a Lorentzian spectral triple (𝒜, ℋ, D, J) whose Dirac operator D has a wave-front set defining a finite propagation speed; the causal order then emerges from the algebraic automorphism group Aut(𝒜). Lorentz symmetry and Poincaré symmetry are interpreted as residual symmetries — stabiliser subgroups of Aut(𝒜) under spontaneous symmetry breaking. The flow of spectral dimension from macroscopic 3 to ultraviolet 2 is heuristically linked to optimal fractal compression of directional information, though no specific functional form is derived. For temporal evolution, we discuss the Tomita–Takesaki modular flow as a candidate algebraic time arrow. A simple non-commutative torus toy model illustrates the operational feasibility of the framework. This programme is exploratory: it does not claim a complete, computationally predictive physical theory, but aims to provide a concrete algebraic language for the direction "causality precedes geometry". Open problems, mathematical challenges, and connections to existing approaches (non-commutative geometry, causal set theory, algebraic quantum field theory) are explicitly identified.