Gravity from Deployment Imbalance: Projective Pre-Closure of DDT Stage-3

This paper develops the Stage-3 gravitational sector of Dimensional Deployment Theory (DDT). DDT posits that the observable three-dimensional spatial regime is not a primitive background, but an operational phase "deployed" from a lower-dimensional projective substrate. In this framework, gravity is not assumed as Newtonian attraction or Einsteinian curvature; instead, it is derived as the operational metric reading of the relaxation of deployment imbalance within a projective vacuum. Theoretical Framework: The Deployment Field: The theory defines a native logarithmic field Φ = ln X², with a locked vacuum state Φᵥ = ln(ln 2). Source of Gravity: Gravity arises from a non-uniform state (u = Φ − Φᵥ) representing projective imbalance energy. Matter is treated not as a primitive source, but as a stable topological packaging of the vacuum. This allows for the interpretation of "apparent gravity without visible matter" as extended deployment imbalance rather than dark matter particles. The Projective Identity: The weak-field coupling is obtained through the projective gravitational identity: π ln 2 G_DDT / c⁴ = 1 This value represents a DDT-normalized coupling. Its conversion to the numerical SI value of Newton’s constant requires a unit-realization map linked to the electron-to-Planck mass ratio. Key Predictions and Observables: Gravitational Waves: Identified as propagating deployment-imbalance relaxation waves. The theory predicts v_GW = c and confirms a purely tensor (spin-2) polarization. Post-Newtonian Parameters: The theory derives γ_PPN = 1 from first principles, successfully reproducing observed light-bending and the Cassini Shapiro-delay bounds without external inputs. Fundamental Constants: DDT predicts two unit-free Stage-3 quantities: α_grav = 2 ln 2 α_grav / α_gauge = 8π The Equivalence Principle: The Weak Equivalence Principle is derived as an exact consequence of the quadratic projective action, making it universal across all topological defect species. Scope and Outlook: The framework defines experimental "closure gates" for inverse-square behavior, free-fall universality, and laboratory determinations of G. It also provides a roadmap for Stage-4 research into particle "unpacking" in colliders, black holes as extreme imbalance objects, and ringdown as relaxation eigenmodes.