Part II: The Connection: Gravity Earned

Part Overview

Part II is the heart of Book V. Gravity is not a force that happens to exist; it is the fourth primitive holonomy sector of the boundary algebra H_∂[ω], canonically determined by the generator α through the Generator–Sector Correspondence. The gravitational constant G is not a fitted parameter: it is a coherence conversion invariant derived from the torus vacuum shape ratio r/R = ι_τ. The τ-Einstein equation is not a partial differential equation on a background manifold: it is a boundary-character identity R^H = κ_τ · T expressing curvature and matter as ω-germs in the same holonomy algebra.

Ten chapters trace the complete gravitational arc:

Chapter 11 (Frame Holonomy Sector) earns gravity as the canonical gap in the D-sector of H_∂[ω], derives G = (c³/ℏ) ι_τ², and establishes the σ-equivariance of κ_τ.

Chapter 12 (Lorentz Without Minkowski) derives Lorentz covariance as a theorem about readouts, not an axiom about spacetime.

Chapter 13 (The τ-Einstein Equation) presents the central equation of τ-gravity as a boundary-character equality and recovers G_{μν} = (8π G/c⁴) T_{μν} as its chart shadow.

Chapter 14 (Linear τ-Einstein) derives the weak-field regime: Mercury’s perihelion, light deflection, gravitational redshift, and gravitational waves—all as linear readouts of the τ-Einstein identity.

Chapters 15–20 complete the arc with the nonlinear regime, Schwarzschild geometry, the TOV equation, calibration, and the gravitational closing identity α_G = α¹⁸√3(1 - (3/π)α).

When Part II is complete, gravitational dynamics has been earned—not postulated—from the base τ¹ and the master constant ι_τ.

Chapters

• Chapter 9: The Frame Holonomy Sector: Gravity as Canonical Gap
• Chapter 10: Lorentz Without Minkowski: Constraint Geometry
• Chapter 11: The τ-Einstein Equation: Boundary-Character Equality
• Chapter 12: Linear τ-Einstein: Weak-Field Regime and Classical Tests
• Chapter 13: Nonlinear τ-Einstein: Address Resolution, Not PDE Solving
• Chapter 14: The τ-Schwarzschild Readout: Torus Vacuum
• Chapter 15: TOV Existence and the Star Builder
• Chapter 16: TOV Phase Boundary and Forced Topology Relaxation
• Chapter 17: The Calibration Triangle: Neutron →
• Chapter 18: The Gravitational Closing Identity