Causality Without Time: A Definability No-Go Theorem and the Minimal Order Framework

This work articulates a structural boundary of causal discourse by establishing a definability no-go result once temporal primitives are removed. It shows that, in the absence of time, causal predicates cannot be coherently grounded in temporal precedence, dynamical dependence, or probabilistic asymmetry alone. The analysis demonstrates that a minimal strict partial order is not a derived feature but a necessary admissibility condition for causality to retain determinate meaning. The result does not propose a physical mechanism or model, but clarifies the weakest structural residue under which causal discourse remains well-formed without reference to time. This manuscript is a preprint and has been submitted for consideration to Foundations of Physics. It has not undergone peer review.