Executable Gauge-Running Hardening of the QDL–SO10–1 Grand-Unification Benchmark: Revised Coupling Closure, Calibrated Threshold Targets, and Proton-Decay Rescaling

The QDL–SO10–1 grand-unification sequence defines a closure-first SO(10)-compatible benchmark within the Quantized Dimensional Ledger (QDL) program. The first three papers in the sequence established a fixed numerical benchmark, its low-energy phenomenology, and a robustness/failure-mode audit. The present paper begins the executable hardening sequence. This paper provides the v0.2 executable gauge-running hardening result for QDL–SO10–1. The v0.1 artifact showed that the original declared target αU−1=25.6\alpha_U^{-1}=25.6αU−1=25.6 is not reproduced by the minimal pure-gauge executable scaffold, yielding an old-target RMS residual of 18.92788118.92788118.927881. The v0.2 artifact resolves the dominant residual by revising the executable coupling target to the mean Pati–Salam inverse coupling at MUM_UMU, giving αU,v0.2−1=44.501718\alpha_{U,\mathrm{v0.2}}^{-1}=44.501718αU,v0.2−1=44.501718 and αU,v0.2=0.022471\alpha_{U,\mathrm{v0.2}}=0.022471αU,v0.2=0.022471. The remaining channel splittings are recorded as calibrated high-scale threshold targets: λ4CU,v0.2=−1.284227\lambda_{4C}^{U,\mathrm{v0.2}}=-1.284227λ4CU,v0.2=−1.284227, λ2LU,v0.2=+0.950018\lambda_{2L}^{U,\mathrm{v0.2}}=+0.950018λ2LU,v0.2=+0.950018, and λ2RU,v0.2=+0.334210\lambda_{2R}^{U,\mathrm{v0.2}}=+0.334210λ2RU,v0.2=+0.334210. With these revised values, the calibrated residual is 2.57×10−72.57\times10^{-7}2.57×10−7. Proton-decay exposure is also rescaled because gauge-mediated lifetimes scale approximately as τp∝αU−2\tau_p\propto\alpha_U^{-2}τp∝αU−2, moving the central p→e+π0p\to e^+\pi^0p→e+π0 lifetime to 3.324041×10353.324041\times10^{35}3.324041×1035 yr. This is a calibrated executable closure result, not yet a full scalar-derived resolution. The next artifact, v0.3, must derive the calibrated threshold offsets from explicit SO(10)→\rightarrow→Pati–Salam scalar multiplets and Dynkin-index weighted threshold corrections. The final all-inclusive QDL–SO10–1 perspective is deferred until the executable hardening sequence is complete.