We propose a microphysical completion for the scalar sector of dilatonic gravity by identifying the dilaton with the coarse-grained stiffness mode of a constrained complex tension field defined on a discrete relational network. Under a controlled ordered-regime coarse-graining, the real projection of the tension scales as Φ(Θ)=Φ0cosΘ, so the Planck mass varies with the phase angle Θ and the Einstein-frame canonical scalar becomes φ∝lnΦ(Θ)/Φ0. This logarithmic structure emerges naturally from the Weyl map and provides the correct canonical variable for vacuum models inspired by the Logarithmic Schrödinger Equation (LogSE). We outline how this scalar–tensor interface can satisfy Solar-System constraints through environmental locking and discuss avenues for laboratory and astrophysical tests based on stiffness–coherence coupling. This paper does not introduce a new scalar–tensor EFT class as such; rather, it provides a controlled microphysical origin for a specific scalar stiffness law, Φ(Θ)∝cosΘ, and for the resulting logarithmic Einstein-frame canonical structure.
Vaillant et al. (Mon,) studied this question.
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