Complete Rate–Distortion Phase Diagram of Haar Oriented Two-Planes: One-Change Hypergeometric Coefficients, Unique Coexistence, and No Reentrance
Let W=x wedge y be the signed unit Pluecker coordinate of a Haar oriented two-plane in R^n, and let reproduction range over the full posterior-mean body under squared ambient loss. An all-field extremum theorem reduces its unrestricted Shannon rate–distortion function to a scalar radial free energy with q=n-2 and overlap normalizer L_q(kappa)=q! sum_{j>=0} kappa^(2j)/(q+2j)!. We solve the remaining global phase problem in every dimension. For the Turanian-like combination J_q=L_q L_q' - kappa L_q L_q'' + kappa(L_q')^2, every coefficient is expressed through the variance of a central parity-truncated binomial law. Likelihood-ratio ordering and an exact uniform tail bound prove one coefficient sign change for every q>=4. Consequently the stationary curve has exactly one fold, the zero and positive phases have exactly one coexistence contact, and no later exchange or radial reentrance is possible. The RDF is an explicit linear face followed by one covariant branch for every n>=6; together with the continuous cases n=3,4,5, this completes the all-dimensional phase diagram. We also derive sharp large-dimension expansions for the coexistence field, active radius, distortion, and information, including the logarithmic finite-size displacement. As operational corollaries, the same RDF equals the minimum worst-source channel capacity, arbitrary joint N-letter classical memories cost N R_n(D), and the iid Haar source has constant tilted information and zero dispersion. The N-letter identity is a mutual-information/capacity theorem, not an exact finite-codebook achievability result. The work concerns signed Pluecker-coordinate compression, not quantum rate–distortion or Born-probability prediction.