Microscopic Origin of Black Hole Entropy from Internal Topological Winding in the Zhang Effective Metric

The Bekenstein-Hawking entropy, which scales with the horizon area rather than volume, remains one of the deepest mysteries in quantum gravity. In this paper, we derive the area law within the rotational-order geometric unification framework based on the Zhang Effective Metric. We identify the four-dimensional event horizon as a topological phase boundary where the internal S³ orientation field reaches a critical configuration, freezing the internal fibre. Evaluating the Gibbons-Hawking-York boundary term of the higher-dimensional Einstein-Hilbert action, we show that the internal extrinsic curvature vanishes, leaving a purely four-dimensional boundary action. Through the Euclidean on-shell action, we rigorously recover the area law S = A/4G. The topological winding number provides a qualitative mechanism for this holographic projection, ensuring that only surface states contribute to the entropy. This provides a fundamental geometric microscopic origin for black hole entropy without invoking string microstates or discrete spin networks.