Data and code for: One quarter, three families: quantized flavor, grand unification, and a magnetic origin in minimal-Yukawa SO(10)

The benchmark global fits of the minimal $10_H + \overline{126}_H$ Yukawa sector of SO(10) contain a hidden regularity. Their fitted matrices decompose as $|Y_{ij}| = c_{ij}\,|Y_{33}|\,\varepsilon^{\,q_i+q_j}$ with one expansion parameter, $\varepsilon = 1/4$, and two integer charge vectors, every constrained coefficient of order one under a stated factor-of-three convention. This two-vector reading is a model-building hypothesis: the fits admit it, but at matched parameter count they do not separate it from a single-vector reading, which is not excluded. We re-fit the sector with the structure imposed and $\varepsilon = 1/4$ frozen, and the full 18-observable GUT-scale menu still closes within $3\sigma$ in both the supersymmetric and non-supersymmetric models. A counting mechanism fixes the quarter: a democratic clockwork chain whose hop has subleading eigenvalue $1/(N_f+1)$, one quarter for three families, under one stated condition on the flavon sector. The same texture supports a candidate non-supersymmetric completion in which two-loop unification selects the seesaw scale the flavor fit requires, with proton decay within Hyper-Kamiokande reach. A density-matrix treatment of its seesaw sector establishes the baryon-asymmetry mechanism, hybrid $N$-plus-triplet leptogenesis, but predicts no value. The cosmology then follows with no adjustable parameter. The mass sum sits at the upper edge of the current $\Lambda$CDM posteriors, and we measure its clustering differential against the minimal-ordering reference in paired simulations at the two-per-mille level (seed error; systematics-limited); a $\Lambda$CDM mass-sum bound a few meV below the fitted point would exclude it. Varying the family number and the internal register dimension of the counting's speculative magnetic-first origin turns the construction into a lattice of counterfactual universes, and we evolve its cells through their own thermal histories. The six computed neighbors all die, in two epoch classes. The home cell is the lattice's one historiogenic cell, the only computed universe that can generate and keep a history: stable matter, an oriented arrow of time, and retained records at once, a convention-conditional uniqueness developed in a companion paper. The sharpest near-term tests are the $\theta_{23}$ octant, the mass sum, and the texture-fixed proton-decay branching pattern.