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.
Patricio E. Valenzuela (Tue,) studied this question.