Black Hole Horizons as Saturation Conditions of the Embedding: A Variational Derivation of Holographic Entropy from the Absolute Frame Theory

June 2nd, 2026: Preprint for consideration at Foundations of Physics. We derive black hole horizons as the active set of a constrained variational problem within the Absolute Frame Theory (AFT). The first axiom of AFT, which quantizes the integrated interaction Lagrangian over four-volumes in units of /2, is reformulated as a continuous bound on the local density of action. Parsimony in conjunction with the absence of additional identifiable constants of the framework fixes this density bound to the topological tension T₀ of the embedding up to a dimensionless factor of order unity. Application of the Karush-Kuhn-Tucker (KKT) conditions to the resulting constrained variational problem yields a codimension-one surface where the constraint is active. This surface is identified with the event horizon. The identification reverses the standard causal arrow of general relativity: saturation of the embedding constraint is primary, and high curvature is its observable manifestation in the four-dimensional manifold. From this structure we derive the holographic scaling S A of the horizon entropy directly, without invoking holographic principles as input. The exact Bekenstein-Hawking coefficient 1/4 is not fixed by the framework; rather than a quantity left for later computation, we conjecture it to be an A-internal constant that is structurally non-identifiable from observations internal to M in the operational Fisher-information sense, the parameter-level counterpart of the G\"odelian epistemic limit of the program; neither work treats this coefficient specifically, so the statement is a structural conjecture. We discuss four discriminating predictions: holographic exactness, logarithmic corrections specific to AFT, a discrete mass spectrum at the Planck scale, and information preservation through the dual KKT multipliers, which provides a structural resolution of the information paradox of Hawking. The construction is fully consistent with the emergence of gravity from the embedding established in companion work.