UV Completion and Horizon Locking in the P2 EFT: A Working Note

We identify a research direction emerging from the covariant EFT formulation of Whitmer (2026c). Two structural features of the action, the sound speed divergence at τ = 1 and the locking of K(X) and V(φ) through H(z), are proposed to share a common origin in the modular Hamiltonian of the Hubble horizon. If correct, this provides a fourth independent derivation of a₀ = cH/2π from horizon causality alone and identifies UV completion as already implicit in the causal structure the EFT inherits. The eigenvalue spectrum calculation confirming this identification is deferred to future work. The sine-Gordon periodicity in V(φ) may emerge as a consequence of the discrete spectrum of K_mod, resolving the principal open question of Whitmer (2026c). This is a working note documenting a proposed direction, not a completed derivation.