The Form and the Strength of Induced Gravity on the Selection–Stitch Lattice: Covariance from Maximal Entropy, Newton's Constant from Maximal Entanglement

In the Selection–Stitch Model (SSM), space is a lattice of entangled bonds. The vacuum's quantum fluctuations, which we call the ocean, induce the Regge action on this lattice if they are covariant. This paper asks why the ocean is covariant and what fixes Newton's constant. We answer both with two forms of one principle. First, maximal entropy. At fixed density, the most random placement of the ocean's degrees of freedom is a Poisson process. If its couplings also keep no memory of an earlier geometry, its vacuum energy can depend on the metric only through the volume. The ocean then sees the lattice's geometry but not its directions, and the graviton stays massless. Numerical tests confirm this. A sprinkled ocean responds to a shear at 1.001 ± 0.002 of the covariant value. The same operator on the lattice gives 1.23, and a memory μ of an old geometry gives exactly 1 − μ. The same ocean has no density halo around a defect, so the field of a mass is carried by the geometry. Second, maximal entanglement. The bonds carry the vacuum's entanglement. If each bond's entanglement follows its share of area, entanglement equilibrium is the Hamiltonian constraint. A solved defect slice satisfies it ball by ball, to within 5% once the ball spans two lattice spacings. If the bond density maximizes the entanglement per unit area, that maximum is 1/4G. A two-qubit bond whose coupling grows with its dual area realizes this law. Since the bonds are frozen ocean, the ocean's stiffness and the bonds' entanglement are one quantity.