This paper establishes the boundary time-readout theorem in the Algebraic Quantum Morphogenesis (AQM)framework and gives a conditionally closed explanation of the Hubble tension. Previous papers have separately established the finite-dimensional spectral neck algebra,measurement as center splitting,the K-flow three-step condensation path,the Standard-Model algebra,boundary-center response,the dark-energy suppression chain,the boundary spectral-closure functor,and the emergence of a three-dimensional spatial spectral dimension.The present paper addresses the next layer:after the threedimensional low-energy spatial spectral shell has been closed,how does the time field arise from boundary readout,and why does the present local Hubble reading appear rescaled relative to the CMB-inferred value? The paper first defines the center projection of the third-step completed condensation sector, P3 ∈ Z (Aeff), and defines the third-step condensation progress by ϕ = ρ(P3). The bulk Wilson line W is defined as the readout of the two-boundary connecting channel that has not yet been absorbed by the third-step condensation center. Under the minimal center-readout normalization, ⟨W ⟩ = ρ(1 −P3 ) = 1 −ϕ For multi-branch nonuniform weights,this formula naturally generalizes to ⟨W ⟩ = 1 −ϕeff. The boundary entanglement entropy is then defined as the information cost of the boundary transmission amplitude, SEE := −SPl ln⟨W ⟩, and the AQM time field is defined by T := 1 −e −SEE /SPl . The main theorem is therefore T = ϕ. 1 The revised version adds an explicit dynamical closure for the present condensation progress.Define the third-step effective condensation integral I3 = ∫ttst0art Γe3ff (t)dt, ϕ0 = 1 −e −I3 In boundary-center record readout,the full stable record length after last scattering is Θfull := ln(1 + zdec). The low-redshift Hubble readout couples only to one manifest center component among the three Z3 centers,hence IH3 = ΘH = 13Θfull , TH0 = ϕH = 1 −e −ΘH = 1 − (1 + zdec)−1/3 . (0.10) If the local boundary clock τ and the bulk/CMB modular time t satisfy dτ = T dt then Hlocal = HCTMB . With zdec = 1089 .92 and H0 ,CMB = 67 .4 one obtains TH0 ≃ 0.90286, HA0,QMlocal ≃ 74.65 This paper does not claim to derive a complete Lorentzian spacetime,the Einstein equation,or a full reconstruction of all cosmological parameters from finite algebra alone.Its scope is the conditional closure of the AQM boundary time-readout mechanism and its conditional explanation of the Hubble tension.