Auditing Holographic Entanglement Entropy: A Quantitative Anatomy of the Ryu-Takayanagi Prescription

I subject the Ryu-Takayanagi (RT) prescription for holographic entanglement entropy to the same hypothesis-led audit previously applied to entanglement equilibrium, mutual information reconstruction, and random tensor networks. The prescription is decomposed into six falsifiable hypotheses T1 to T6. The main findings are: On the exactly solvable AdS3/CFT2 Poincare disk we verify the geodesic-length formula, its logarithmic coefficient (Brown-Henneaux matching), and characterize the mutual-information phase transition quantitatively. The transition sits at cross ratio xc = 1/2 + O(exp(-2rho)), exactly at alpha_c = pi/2 for all rho in the antipodal-symmetric family, with randomized-asymmetric deviations vanishing exponentially with cutoff depth rho, showing that the universal CFT2 location is the asymptotic limit of the bulk criterion, not an identity at finite cutoff. The homology constraint, often presented as an output of the holographic setup, is shown to be an input: it must be imposed by hand on the graph, and the phase transition it produces is first-order-sharp at the RT level while any discretization smears it. The continuum limit of discretized RT surfaces fails to be Riemannian: polar-lattice min-cuts converge, under delta-refinement, to a Finsler (taxicab-normal) metric with a systematic, delta-independent offset of +4.5% at 60 degrees, +13% at 30 degrees, +18% at 15 degrees, and -0.1% at 90 degrees. Mutual information, a difference of areas, amplifies these offsets asymmetrically: the connected-phase signal is underreported by up to 24% at delta = 0.1, while the transition window fabricates spurious mutual information of +0.39 at delta = 0.2. I conclude that RT is exact as a formula, input-carrying as a prescription, and metric-blind under discretization, with the error concentrated precisely at the shallow geodesics where the prescription is most often probed. All numbers are generated by two deterministic Python programs with no Monte Carlo required.