Modified Background Expansion, Sound-Horizon Transport, and the Hubble-Tension Interface in the Finite-Capacity Latency–Erasure Theory

We construct the first explicit Hubble-sector interface of the finite-capacity latency–erasure theory by deriving its modified background expansion and early-universe sound-horizon transport structure in a form suitable for quantitative confrontation with the Hubble tension. Earlier FCLET studies established the strong-field shell benchmark, detector-facing ringdown confrontation logic, the primordial tensor corridor, the shell–cosmology bridge, the microstate completion of the burden–latency–overwrite framework, and the first reduced and true global survival geometry linking strong-field and cosmological sectors. What remained absent was a closed background-level derivation of the Hubble interface itself. In particular, the program already possessed a viable tensor-sector mechanism and a plausible transport-channel route through which finite-capacity saturation can renormalize the sound horizon, but it did not yet possess a full FCLET background equation for , nor a quantitative derivation of how that modification propagates into the inferred late-time Hubble scale. The present article provides that derivation. The paper proceeds in three stages. First, we derive the effective FCLET background equation by introducing a saturation-weighted correction to the homogeneous cosmological evolution law, expressed through the finite-capacity load variable and its associated latency functional. Second, we derive the acoustic transport sector and show how a finite-capacity correction to the pre-recombination sound speed modifies the sound horizon, thereby shifting the CMB-inferred Hubble scale even when the late-time expansion history remains near standard form. Third, we combine the background and transport sectors to obtain a quantitative FCLET mapping and identify the parameter region in which the theory can reduce the sound horizon enough to move the inferred Hubble scale upward without destroying the cosmological corridor already established in Article 89. The result is not a loose qualitative claim that FCLET may influence the Hubble tension. It is the first closed Hubble-interface derivation of the program. The paper distinguishes sharply between two mechanisms: genuine background modification through the FCLET effective Friedmann sector, and transport-only renormalization through the pre-recombination sound speed. This distinction is decisive because the theory need not solve the Hubble tension by a brute-force late-time expansion anomaly. It may instead act by a controlled early-universe saturation correction that leaves the tensor corridor and the global viability map intact. The outcome of the article is therefore a quantitative FCLET prediction for whether the theory merely relaxes the Hubble tension or can genuinely shift the inferred into the local-measurement range.