The Mittermeier Attractor Tension Geometry: A Closure-First Rank-One Covariance Vector for the Planck–DESI–SNe–Growth Displacement

The present cosmological data landscape is not defined by a single discrepant number, but by a correlated displacement between the CMB-inferred early-universe coordinate system and the late-time coordinate system constrained by BAO, supernova and growth observations. This companion formulates the Mittermeier Attractor Theory (MAT) contribution to that problem as a closure-first rank-one tension geometry. The active MAT branch transports one chart residue into two matter projections: a CMB-facing primordial-transfer coordinate and a late-time proper-time/BAO/SNe/growth coordinate. Numerically, the resulting values Ω_ (m, P) * = 0. 31514108474281916 and Ω_ (m, D) * = 0. 298052439439386 lie directly in the Planck 2018 and DESI DR2 reference corridors, respectively. Their separation is not introduced as a fitted shift. It is the exact active-branch identity ΔΩₘ* = Ω_ (m, P) * − Ω_ (m, D) * = (9/8) δα_ (chart, π) * = 9/ (8 N_*MAT). The same displacement propagates into physical matter density, matter-radiation equality, the transfer-function turnover scale, the Hubble denominator and the projected S₈ direction. MAT therefore predicts a rigid multi-observable vector rather than independent parameter shifts. The paper isolates the corresponding covariance test: given an empirical displacement vector and its covariance matrix, the C^ (-1) -weighted angle to the MAT vector supplies a direct falsification criterion. Near-alignment would indicate that the current early–late mismatch follows the MAT projection geometry; a low alignment would reject the rank-one hypothesis. The result is a parameter-free algebraic coordinate system for the Planck–DESI–SNe–growth tension surface, with the covariant microscopic realization left as the next completion target.