A Dual-Lattice Resolution of the Hubble Tension via Logarithmic Constraint Relaxation

Theory v2.0 materials developed by Moses Kelley, including the v2.0 correction note and associated theoretical framework resolving the Hubble tension.\
The PCP‑Lattice framework models the quantum vacuum as a dual‑lattice gauge system whose global consistency is verified in the sense of Probabilistically Checkable Proofs (PCP). In the corrected v2.0 formulation, the late‑time Hubble parameter is not modified by a direct PCP error factor (as in v1.0), but instead by a logarithmic coupling between dual‑lattice determinant evolution and effective energy density. This yields the master relation
[H_{\text{local}} = H_{\text{early}} \bigl[1 + \frac{\xi}{2}\ln(\det \Lambda^*_{\text{now}}/\det \Lambda^*_{\text{then}})\bigr]] with [\xi \approx 0.41] and a calibrated dual‑lattice volume ratio [R_{\det} \approx 1.507], corresponding to a 50.7% increase in dual‑lattice volume between recombination and today. The resulting prediction [H_{\text{local}} = 73.01 \pm 0.47] km/s/Mpc agrees with SH0ES [H_0 = 73.04 \pm 1.04] km/s/Mpc to within 0.03σ while remaining anchored to a Planck‑like early‑universe value [H_{\text{early}} = 67.36 \pm 0.54] km/s/Mpc.\
The record also includes a fiducial redshift‑dependent H(z) model in which the integrated constraint‑relaxation effect is realized as a smooth correction to a ΛCDM background, parametrized by a transition redshift [z_t \approx 0.7] and a sharpness index [n \approx 2]. This model predicts: (i) a modest [\sim -0.3\%] shift in the BAO sound horizon, (ii) a few‑percent modification of luminosity distances and distance moduli for Type Ia supernovae around [z \sim 1], (iii) percent‑level differences in cosmic‑chronometer H(z) measurements compatible with current data, and (iv) an 8.4σ discriminant between PCP‑Lattice and Planck‑ΛCDM using low‑redshift gravitational‑wave standard sirens.\
Together, these materials provide a self‑contained specification of the PCP‑Lattice v2.0 theory, the corrected Hubble‑tension resolution mechanism, and its main astrophysical, experimental, and computational applications