FCLET Acoustic Transport in CLASS

We establish the background acoustic transport branch of the finite-capacity latency–erasure theory in CLASS and show that it produces a controlled contraction of the sound horizon while preserving the exact CDM limit. The central physical statement is that the early photon–baryon medium is not required to propagate acoustic information with the standard transport efficiency once the universe is treated as a finite-capacity system. In the FCLET framework, acoustic propagation is burdened by a transport factor where is a cosmological burden functional and is the transport sensitivity parameter. This factor moderates the sound speed directly and therefore contracts the acoustic ruler at the level of background transport itself rather than through a post hoc rescaling. We implement this structure in CLASS at the background and thermodynamic levels through the exact map This formulation yields a fully controlled acoustic branch: the drag-epoch sound horizon is reduced in the phenomenologically correct direction, while the theory contains CDM exactly as its zero-burden submanifold. The modified branch is therefore not merely close to standard cosmology in a suitable limit; it recovers the standard branch exactly. The paper develops the full background transport logic, defines the burden functional and its admissible limits, derives the thermodynamic completion of the acoustic sector, and presents the corresponding CLASS implementation architecture. A representative locked benchmark yields a sound-horizon ratio in the neighborhood of demonstrating a controlled reduction of the ruler while preserving exact standard-limit recovery. This background branch already moves cosmological inference in the higher- direction, but it does not by itself solve the observable perturbative transmission problem. The transmission of the burdened ruler into the TT hierarchy is developed in the companion perturbation paper, while the constitutive radiative-memory completion of that perturbative branch is established in the subsequent microphysical completion paper. This paper therefore establishes the background acoustic transport branch of FCLET in CLASS with exact CDM limit recovery and a controlled contraction of the sound horizon.