Introduction and principal results

A consistency condition on a rewrite system can preserve an event order: incompatible dependencies are excluded, independent operations commute, and records do not depend on their legal interleaving. The further claim that this mechanism selects a Lorentzian light cone requires additional mathematics.

A scheduler chooses an evaluation order. Interchanging independent reductions does not, by itself, define a boost, a linear action on events, or a transformation of clocks and rulers. Distributed computation already provides a setting in which causal ordering is meaningful without a spacetime metric Lamport.

This paper gives an obstruction theorem and a matching conditional representation theorem. The latter uses an established cone classification, not a new characterization of Lorentz cones. Its contribution here is the precise separation of the operational premises from the geometric hypotheses required to apply that classification.