We establish the perturbative discovery branch of the finite-capacity latency–erasure acoustic program and show that background sound-horizon contraction alone does not suffice for observable TT peak displacement. The preceding background-transport paper demonstrated that FCLET burdens the acoustic ruler through a transport factor acting on the photon–baryon sound speed, thereby contracting the sound horizon with exact CDM limit recovery. The unresolved problem is whether that burdened ruler is automatically transmitted into the scalar CMB hierarchy. It is not. A reduced sound horizon does not by itself force a shifted first TT acoustic peak. A distinct perturbative phase carrier is required. We construct a controlled diagnostic program inside CLASS to identify that carrier. The background branch is treated as the exact control sector. We then distinguish two qualitatively different perturbative responses. Source-dominated modifications produce amplitude suppression without stable phase transport; they define a damping branch. By contrast, modifications acting on the restoring structure of the scalar photon hierarchy produce a genuine rightward displacement of the first TT peak; they define an oscillator branch. The observable acoustic phase is therefore carried not by generic damping, but by an effective scalar operator acting on the restoring sector of the photon hierarchy. The diagnostic program isolates a split perturbative continuation structure with a phase continuation coefficient , a source continuation coefficient , and an exact photon momentum-side normalization The resulting effective phase-carrier replacement is The first stable effective implementation is locked at and yields the first stable observable checkpoint This paper therefore closes the discovery phase of the FCLET perturbation program. It identifies, isolates, and locks the first stable effective scalar phase carrier required to transport the burdened acoustic scale into the observable TT hierarchy. The constitutive derivation of this operator is developed in the companion microphysical completion paper.
Ali Caner Yücel (Sat,) studied this question.