Geometric Self-Consistency (TAG): the geometric–dynamical branch of Transition Information Geometry

We present TAG (Teoria da Autoconsistência Geométrica, Geometric Self-Consistency), the geometric–dynamical branch of Transition Information Geometry (GIT). Where GIT is kinematic—specifying what the universe is, starting from mutual information I organized by a logarithmic spiral—TAG supplies the equation of motion: how that structure moves. TAG has its own scalar–tensor action, its own field equations, and is subordinate to GIT through a precise physical asymmetry (the Born mirror). The engine of all its dynamics is a single arrow of time, identified with the real part λ of the spiral generator. We argue that one action, driven by one arrow, yields galaxies, the organization of matter, Planck-star cores and the fractal structure of the cosmos—several scales, one background object (the holographic grain, a sphere of area 4πℓP² carrying a Z₃ phase), with zero continuous free parameters. The same discharge curve runs from the atom (ultraviolet) to the galaxy (infrared). We give falsifiable predictions: the speed of gravitational waves equals the speed of light exactly (confirmed by GW170817/GRB 170817A) ; the gravitational slip vanishes on linear scales (testable by Euclid/LSST) ; the primordial non-Gaussianity has relative strength fNL ~ 0. 2 rather than the slow-roll ~0. 05 (testable by CMB-S4/LiteBIRD) ; and the fractal dimension of the underlying interference object is df = log₂3 ≈ 1. 585. The conformal-mode (measure) problem is resolved by reading that mode as the time axis. We are explicit throughout about the distinction between structure (dimensionless, derived) and ruler (the dimensional conversion at the destination).