This paper presents a minimal formal framework in which time is not assumed as a primitive quantity but is derived as a representation of ordered state transformations. Starting from states and a single state transformation, an intrinsic order and semigroup evolution arise necessarily. Non-invertibility is treated as an admissible structural feature, leading to non-unique retrodiction and an intrinsic forward/backward asymmetry. Time is introduced exclusively as a coordinate representation of this order. No physical laws, geometric assumptions, or empirical claims are employed. The work is intentionally structural and representational, clarifying which aspects of temporal description are invariant and which depend on parametrization.