Closure-First Resolution of the Hubble Tension in Mittermeier Attractor Theory: Hubble-Branch Geometry, the Planck–DESI Matter Split, and the Active Vacuum Readout

The present discrepancy in the cosmic expansion rate, known as the Hubble tension, is treated in the standard ΛCDM paradigm as a scalar conflict between early-universe calibration and local distance measurements. This paper demonstrates that this conflict is a mathematical artifact produced by compressing distinct geometric readout lanes into a single scalar H₀. Within the axiomatic Mittermeier Attractor Theory (MAT), we present a deterministic, parameter-free closure-first resolution. The vacuum closure condition δ₃ (Λ₀*) = 0 strictly determines the active vacuum point Λ₀* ≈ 2. 817 × 10^ (-122) and a universal chart residue δα_ (chart, π) * ≈ 0. 01519. From this single residue, exact affine projections generate both the CMB-facing matter density Ω_ (m, P) * ≈ 0. 315141 and the late-time proper-time density Ω_ (m, D) * ≈ 0. 298052. Their separation is governed by the exact active-branch identity ΔΩₘ* = (9/8) δα_ (chart, π) *. Inserting the late-time density into the closed Friedmann denominator yields a native proper-time expansion rate of H₀* ≈ 66. 2020 km s^ (-1) Mpc^ (-1). The Hubble tension is thus internally resolved as readout-lane conflation. The same late-time branch also fixes the smooth-gate linear perturbation sector: structure growth is propagated on the native late-time matter lane, with its source set by the MAT matter history and its damping set by the MAT Hubble-friction history, while the conventional S₈ scaling is retained only as a fixed-amplitude audit coordinate. Consequently, the growth sector supplies an additional covariance direction of the same closure residue rather than an independent fitted amplitude. The resulting theory defines a deterministic, overdetermined multi-probe displacement vector, tied to the same vacuum residue that fixes Λ₀*, Ω_ (m, P) *, Ω_ (m, D) *, and H₀*. External falsification is therefore not organized around isolated point-value comparisons, but around full covariance alignment, cos (θC), against the combined Planck–BAO–SNe–growth–chronometer data space.