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May 13, 2026Open Access

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

Key Points

This work aims to develop the gravitational sector of Dimensional Deployment Theory and reinterpret gravity's nature.
Developed a theoretical framework grounded in a logarithmic field representing projective imbalance energy.
Derived weak-field coupling and identified gravitational waves as deployment-imbalance relaxation waves.
Generated key predictions such as light-bending effects and derived parameters from foundational principles.
Gravitational waves predicted to have a speed equal to light (v_GW = c) with purely tensor polarization.
Successfully derived light-bending and Shapiro-delay bounds consistent with observations, maintaining γ_PPN = 1.
Predicted unit-free gravitational and gauge quantities, asserting a universal equivalence principle across topological defect species.

Abstract

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 GDDT / 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 vGW = c and confirms a purely tensor (spin-2) polarization. Post-Newtonian Parameters: The theory derives γPPN = 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: αgrav = 2 ln 2 αgrav / αgauge = 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.

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