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. 6U^-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 MUMUMU, giving αU, v0. 2−1=44. 501718ₔ, ₕ₀. ₂^-1=44. 501718αU, v0. 2−1=44. 501718 and αU, v0. 2=0. 022471ₔ, ₕ₀. ₂=0. 022471αU, v0. 2=0. 022471. The remaining channel splittings are recorded as calibrated high-scale threshold targets: λ4CU, v0. 2=−1. 284227₄₂^U, v0. 2=-1. 284227λ4CU, v0. 2=−1. 284227, λ2LU, v0. 2=+0. 950018₂₋^U, v0. 2=+0. 950018λ2LU, v0. 2=+0. 950018, and λ2RU, v0. 2=+0. 334210₂ₑ^U, v0. 2=+0. 334210λ2RU, v0. 2=+0. 334210. With these revised values, the calibrated residual is 2. 57×10−72. 5710^-72. 57×10−7. Proton-decay exposure is also rescaled because gauge-mediated lifetimes scale approximately as τp∝αU−2ₚU^-2τp∝αU−2, moving the central p→e+π0p e^+⁰p→e+π0 lifetime to 3. 324041×10353. 32404110^353. 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) →→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.
James D. Bourassa (2026) studied this question.