A Closed Vacuum-to-Cosmology Readout of the Late-Time Vacuum Scale in Mittermeier Attractor Theory: Dimensionless Resolution of the Gravitational Vacuum Hierarchy, Calibrated Closure of Lambda_0, and Transported Matter-Vacuum Predictions

The vacuum catastrophe is the problem that local quantum field theory naturally suggests a gravitational vacuum sector of order unity in Planck units, whereas the late Universe is governed by a vacuum scale of order 10^-122. This companion addresses the gravity-facing part of that hierarchy problem in a form that can be reconstructed from one synchronized source of truth. The central running quantity is λ̂(u) = Λ(u) G(u), where Λ(u) is the running vacuum term, G(u) is the running gravitational coupling, and u is the chart coordinate that measures position along the exact vacuum flow. The problem is therefore posed as a forward calculation: start from a fixed ultraviolet boundary datum, integrate one fixed flow, and determine which late-time dimensionless vacuum scale that flow actually reads out. In synchronized Mittermeier Attractor Theory (MAT), the ultraviolet boundary condition is fixed internally by the Mittermeier Planck-boundary constant κ_M = e^-2 / ρ, with ρ defined by ρ^3 = ρ + 1. Here ρ is the plastic constant. The same boundary seed selects the theory-internal metrological fine-structure branch α_M = κ_M / 14. In the synchronized lane this already fixes the threshold pair through q_M = 28 e α_M = 2 e^-1 / ρ and p_M = q_M / √π, so the plastic-constant lock and the 14-lock are not appended later as interpretive decorations but propagated directly into the exact vacuum flow itself. The corresponding π-manifold chart is fixed by an exact infrared plateau β_∞,π = 3π / 10 and an exact chart slope α_RG,π = 20 / (3π), with α_RG,π β_∞,π = 2. The vacuum lane is then governed by one exact two-threshold flow and its exact back-integration. In that sense, the late-time vacuum value is not inserted as an independent fit parameter after the fact. It is the endpoint of a rigid ultraviolet-to-infrared transport law. The same synchronized architecture also contains a coherent π-dual manifold layer in which the gate, curvature bridge, chart slope, plateau, and late-time projection depths are algebraically linked rather than introduced one by one. This linked closure structure is essential for interpretation: the numerically sharp outputs reported here do not arise as isolated endpoint coincidences, but as repeated readouts of one locked architecture. At the observation-facing benchmark Λ_0 = 2.9 × 10^-122, the synchronized readout yields u_cosmo,π = 299.05635044704695, δα_chart,π = 0.015190721131109086, and δ_3 = 6.069902711019906 × 10^-10. Here δα_chart,π is the realized chart backreaction residue produced by the exact two-threshold flow, and δ_3 is the remaining realized-versus-ideal metrological closure sliver at the observation-facing benchmark. The same rigid architecture then defines a calibrated closure point Λ_0* = 2.816998637863968 × 10^-122, selected by the exact internal condition δ_3(Λ_0*) = 0. In addition, the paper records the explicit structured near-lock approximation Λ_0,NL = 2.816997989820800 × 10^-122, whose mantissa differs from the calibrated value by only M* − M_NL = 6.480431684607879 × 10^-7. The main analytic result is the exact threshold-balance law at the calibrated point together with its controlled large-u expansion. Truncating that expansion at O(u^-2) reproduces the exact balance with residual 5.074873694610460 × 10^-7, showing that the same asymptotic tail that governs the ultraviolet-to-infrared vacuum flow also governs the closure-point analysis. The late-time vacuum hierarchy is therefore no longer treated here as a bare unexplained target. Within the synchronized MAT lane it becomes a reproducible boundary-to-readout calculation with explicit internal audits, explicit claim classes, and direct falsifiability. For standard late-time cosmology, the significance is immediate: if this structure continues to match sharper future determinations of the vacuum scale, the fine-structure constant, and the matter-vacuum sector, then Λ_0 is no longer merely an empirical input but the macroscopic readout of a rigid microscopic-to-cosmological attractor. If it does not, the same many-digit structure makes the proposal decisively testable.