Variational dynamics of the Informational Numerical Space: energetic coherence, informational kink and causal mediation

In [Moya-ENI1, 2026] the Informational Numerical Space (ENI) was introduced as a kinematic structure whose elementary object is the state I₄ = (λ, τ, σ, ι), and the coherence error was shown to take the closed form Δ_E = 2 tanh(|ln(λ/cτ)|/2). This work develops the second level of the programme: an effective variational extension for ENI fields on a given spacetime and its comparison with established physical equations. In the logarithmic variable w = ln(cτ/λ), Δ_E = 2|tanh(w/2)| is independent of the common scale of λ and cτ. Endowing the scale sector with a Fisher metric, with the same statistical family for both scales, we prove that it splits orthogonally into a global scale mode s and an incoherence mode w, with dℓ_F² = 4 ds² + dw². Three consequences follow. The mode s is classically flat and carries a conserved Noether current; its physical status is left open. The mode w obeys a Klein–Gordon equation with m_w² = 2κ_E/K = κ_E/F_I². And, with the coercive potential U_coh = κ_E(cosh w − 1), distinct from the observable Δ_E, the homogeneous mode of w on a prescribed expanding FLRW background whose Hubble rate is eventually confined between two positive constants, with bounded derivative (de Sitter, or a background with a positive cosmological constant), converges to coherence, λ = cτ; in the radiation and matter eras the envelope of the linear regime decays asymptotically as a^(−3/2). In the informational sector, treated as an effective field, the minimal-degree polynomial potential with vanishing energy and force at the extreme states is unique up to a positive factor, U_ι = κ_ι [ι(1−ι)]², and admits a Bogomolny kink of tension √(2κ_ι K_ι)/6; its exact ℤ₂ symmetry ι ↔ 1 − ι is not required by the physical interpretation, and an added entropy-biased-potential hypothesis breaks it, making the pure vacuum of the model metastable. In the discrete causal sector we prove that, per unit hypersurface measure and for equal non-zero local weights, the direct emitter→receiver transition carries twice the quadratic jump penalty of the transition mediated by the neutral state, an inequality of the same form as the complete-wetting condition of three-phase systems. Finally, with a momentum channel introduced in this work, which compares the total energy with the scale pc, the relation E_τ² − E_λ² = m²c⁴ is recovered, coherence being the null mass shell. Each result is classified as an ENI theorem, an inherited result, a reinterpretation of known physics, or an added hypothesis. The record includes the Spanish original, this English version and the verification script eni_A2_verificacion.py (46 symbolic and numerical checks).