Three Roads to S = A/ (2Dₜ lP²): Statistical Mechanics of the Horizon in (6+2) -Dimensional Elastic Spacetime

In a companion paper (Zenodo DOI: 10.5281/zenodo.19160124), we identified the factor 4 in the Bekenstein–Hawking entropy S = kB A/(4 lP²) as 2Dt within the (6+2)-dimensional elastic spacetime theory. Here we provide three independent statistical-mechanical derivations: (I) correlation patches, where Dt = 2 temporal components impose Dt correlation directions on the 2D horizon surface, yielding independent domains of 2Dt cells; (II) entanglement entropy, where each horizon cell contributes Dt channels constrained by the critical-strain condition; (III) a mapping to a critical q = 2Dt = 4 Potts model on the horizon lattice. All three roads converge on S = kB A/(2Dt lP²). We further derive the Page curve in EST, finding the Page time at ~99.8% of the evaporation time (versus ~50% in random-matrix models), with information released in a sharp final burst before a stable Planck-mass remnant. This constitutes a falsifiable prediction distinguishing EST from generic unitarity-restoration scenarios. Zero free parameters.