This work demonstrates a benchmark closure integrating proton decay, flavor, and leptogenesis, highlighting its viability and structural admissibility.
Grand-unified theories are judged by a demanding combination of criteria: group-theoretic economy, matter embedding, anomaly consistency, gauge-coupling behavior, scalar-threshold control, neutrino-mass structure, proton-decay exposure, flavor viability, baryogenesis, low-energy phenomenology, falsifiability, and relation to gravity. The Quantized Dimensional Ledger (QDL) enters this landscape from a different direction. QDL is not presented as a replacement for conventional GUT model building. Its distinct contribution is a structural-admissibility layer upstream of ordinary parameter optimization: physical constructions are assigned integer ledger charges and judged by closure rather than dimensional homogeneity alone. This paper is the integrated executable closure capstone for the QDL–SO10–1 benchmark sequence. It updates and supersedes the earlier historical perspective paper by incorporating the completed benchmark-level hardening sequence. Papers #1–#3 established the initial trilogy: a fixed SO(10)-compatible numerical benchmark, low-energy phenomenology closure, and stress-test / robustness audit. Papers #5–#8 then supplied executable gauge-running hardening, scalar-derived threshold-block closure, operator-level proton-decay exposure, and flavor/leptogenesis hardening with proton-decay feedback. The integrated benchmark retains the chain SO(10) to SU(4)_C x SU(2)_L x SU(2)_R to SU(3)_C x SU(2)_L x U(1)_Y, with M_U = 1.00 x 10^16 GeV, M_I = 4.70 x 10^13 GeV, and revised executable coupling alpha_U^-1 = 44.501718, corresponding to alpha_U = 0.022471. The high-scale neutrino hierarchy is M_N1 = 8.18 x 10^11 GeV, M_N2 = 1.53 x 10^12 GeV, and M_N3 = 4.67 x 10^13 GeV. The flavor and leptogenesis hardening layer gives sum m_i = 0.0617 eV, m_beta_beta = 5.44 meV, m_beta = 9.18 meV, and eta_B = 5.57 x 10^-10. After v0.5 flavor feedback, the benchmark proton-decay lifetimes remain above current bounds: tau(p to e+ pi0) = 2.396423 x 10^36 yr, tau(p to mu+ pi0) = 4.088415 x 10^37 yr, tau(p to anti-nu K+) = 6.459280 x 10^37 yr, tau(p to anti-nu pi+) = 7.170619 x 10^36 yr, and tau(p to e+ K0) = 5.885232 x 10^38 yr. The central conclusion is disciplined but strong: QDL–SO10–1 is not a final theory of nature, not a proof of unique SO(10), not a completed quantum-gravity framework, and not a full global flavor scan. It is, however, now a serious executable closure benchmark. On the scale of benchmark-level grand-unification programs, it merits a 9.0/10 rating: structurally admissible, numerically auditable, scalar-hardened, proton-decay exposed, flavor-tested, leptogenesis-viable, historically situated, and explicitly falsifiable.
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James D. Bourassa (2026) studied this question.
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