Toroidal Bekenstein Capacity, Logical Cycles, and Finite Near-Horizon Reconstruction

We introduce a toroidal representation of Bekenstein capacity for finite near-horizon quantum information. The energy E of a bounded region defines an associated Schwarzschild length rs=2GE/c4, an energy-associated length that need not equal a horizon radius. Together with the operational radius R, it yields the two-cycle capacity area AT=4π2rsR. As a modeling choice, we promote these two physical scales into the noncontractible cycles of a minimal genus-one code support. The result is a finite-capacity toric-code model in which the intersection form fixes the logical algebra, the capacity conditionally bounds admissible microscopic support and code distance, and an explicit two-logical-qubit Clifford model illustrates sequential purifier transfer without double-counting the interior purifier. The same structure gives a laboratory-testable quantum information analogue: anisotropic logical protection and code-deformation transfer in finite surface-code memories.