PFGM Model

I introduce the Proto‑Field Gravity Model (PFGM), a minimalist theory in which a single real scalar generates both matter and geometry. Starting from the Lorentz‑invariant action<br>I obtain the disformal metric. A covariant virial analysis shows that the accompanying quartic‑gradient pressure stabilizes finite‑energy solitons that satisfy the exact balance. Expanding the curved‑index field equations to second post‑Newtonian order I find all conservative weak‑field parameters unchanged from general relativity; the leading deviation appears only in the momentum‑flux coefficient, far below current Solar‑System sensitivity. One‑dimensional simulations confirm horizon‑free, ultra‑compact remnants, while thin‑shell toy models predict late‑time gravitational‑wave echoes with delay. Because gradients of never diverge, curvature singularities are avoided and the theory remains perturbatively well‑behaved up to the strong‑coupling scale. Present astrophysical data leave essentially unconstrained, but sub‑millimeter experiments and strong‑field binaries offer decisive tests. PFGM thus provides an economical yet phenomenologically rich framework warranting further cosmological and quantum investigations.