Gravity as Vacuum Overpressure: A Le Sage Mechanism from Massive Brans-Dicke Scalars

We propose a reformulation of Vacuum Folding Dynamics (VFD) in which Newtonian gravity arises as a net inward force from isotropic vacuum pressure partially attenuated by matter — a modern Le Sage mechanism mediated by a massive Brans-Dicke scalar field. The scalar mass is fixed by a self-consistency condition linking the vacuum pressure to Newton's constant: m_sigma = f(Omega_0), where Omega_0 is the free Brans-Dicke parameter. Because the scalar is massive (Compton wavelength lambda_C ~ 0.1–5 mm at the experimentally accessible sweet spot), solar-system PPN constraints such as Cassini do not apply, and Omega_0 remains free — bounded only by sub-centimetre inverse-square-law (ISL) tests (Omega_0 > ~50). The result is a one-parameter prediction curve in (alpha, lambda) space for a Yukawa-type fifth force, where alpha = 1/(2*Omega_0 + 3) and lambda = hbar/(m_sigma * c). The prediction curve lies a factor 5–20 below current Eöt-Wash torsion-balance bounds in the range lambda = 0.1–5 mm, |alpha| = 10⁻³–10⁻². The model is unscreened (no chameleon, symmetron, or Vainshtein mechanism), making it uniquely testable at laboratory scales. A sensitivity improvement of roughly one order of magnitude in sub-millimetre ISL experiments would either detect or definitively exclude the entire prediction curve. An exclusion plot (Figure 1) shows the VFD prediction curve against current Eöt-Wash bounds. A supplementary experimental proposal for torsion-balance tests is included. v6: Corrected numerical evaluation of Eq. 21 (factor 10 error in denominator), removed erroneous Eq. 26 (alpha_eff), removed inapplicable Cassini constraint, reformulated prediction as one-parameter curve.