The Albertian Horizon: Exceptional Quantum Mechanics and an Obstruction to the AMPS Paradox

The Almheiri-Marolf-Polchinski-Sully (AMPS) firewall paradox assumes a globally associativetripartite tensor-product Hilbert-space structure. In octonionic magical supergravity, the attractormechanism organizes the near-horizon black-hole data in terms of the exceptional Jordan algebraJ3 (O). Motivated by this macroscopic freeze-out, we postulate that the effective horizon sectoradmits an Albertian algebraic quantum description. The attractor fixed-point data is canonicallyAlbertian, and under natural algebraic closure assumptions the corresponding horizon observablealgebra is the unique finite-dimensional exceptional Jordan algebra J3 (O). From this single physicalpostulate, the canonical horizon state space, the cubic invariant, and the Freudenthal covariantenvelope descend constructively. We then prove the Albert-Freudenthal Squeeze Theorem: horizonphysics is squeezed between locally associative sectors, compatible with smooth-horizon effective fieldtheory reasoning and supporting an internal associative radiative channel, and a globally exceptionalsector. Because the Albert algebra does not admit the standard composite structure required bythe AMPS tripartite setup, the corresponding compositional syntax is mathematically obstructed.The resulting algebraic structure obstructs the globally associative tripartite tensor-product syntaxrequired by the AMPS paradox while preserving locally associative sectors compatible with effectivefield theory at the horizon.