Data and code for: Historiogenic universes: which cells of the SO(10) flavor lattice can generate and keep a history

The democratic-clockwork reading of the minimal $10_H + \overline{126}_H$ Yukawa sector of SO(10), developed in a companion paper, quantizes the flavor expansion parameter as the subleading eigenvalue $1/m$ of a family-symmetric hop, so family number $N_f$ and register dimension $m$ decouple into a lattice of cells within one fixed theory, ours the equal-weight point $(3,4)$. This paper surveys that lattice as the phase diagram of the fixed theory. Every computed cell and branch realizes the same symmetry breaking; what distinguishes end states is a level crossing of the lightest baryon, a vacuum-stability class, or an environmental inequality, never a symmetry realization, so no enlargement of the gauge group is needed to host any state found here. The family charge vectors are derived from the chain up to a minimality choice, calibrated at $N_f = 3$ where the construction returns the recorded $q_h = (3,2,0)$, $q_f = (2,1,0)$, and $\eps = 1/4$ with no charge put in by hand; a no-wrap register counting that would replace minimality is stated as a conjecture reduced to a single lift axiom, selecting the same spectrum uniquely at $N_f = 3$ through $6$, agreeing with minimality on the lattice diagonal at every rank, provably beyond the reach of the certified register laws alone, and falsifiable by any consistent sub-diagonal cell. On exact four- and five-family textures the cells $(4,5)$ and $(5,6)$ die at weak freeze-out: the charged nucleon is the heavier member of the lightest doublet in $0.995$ $[0.994, 0.996]$ of calibrated draws at $(4,5)$ and in all conditioned draws at $(5,6)$, both on the primary convention at tolerance 3; over every sampling measure and convention tested at that tolerance the fraction never falls below $0.94996$, the $(5,6)$ value under $\alpha_U$-held anchoring, and the verdict never flips. The mechanism is a family-space fact: our own up quark rests on a coefficient cancellation of about one part in eighty that the deep families of those cells do not inherit, and the two Higgs-channel contributions add rather than cancel. In $0.38$ to $0.53$ of $(4,5)$'s calibrated draws the ground-state baryon carries charge $-1$, and the resulting charge-conjugated hydrogen branch survives every gate this programme can compute, at strict same-criteria probability bracketed $[0.00, 0.14]$ by the deuteron-binding literature, $0.131$ under the favored response form at the recorded pion treatment. The open structural channel is the branch's split pion multiplet. Exact spin-flavor algebra makes the mirror nucleon pair $\Sigma$-like, cutting the charge-exchange coupling to $4$ to $7$ percent of the prior pricing and the total exchange coupling to $0.28$ to $0.39$ of our deuteron channel's, and a deuteron-calibrated leading-order model then places the split system below both endpoint pricings; the residual binding is contact-dominated, so the deciding computation is a lattice two-baryon calculation with non-degenerate light quarks, a configuration nothing in the current literature covers, specified here to deliverable level. The home cell's uniqueness on the computed table is therefore convention-conditional. A record axis is computed for every cell from two integers, and the pure-gauge $N_f = 0$ row bounds it from below: a real universe with a glueball dark sector and a complete holonomy archive, anepigraphic in the sense defined here, with maximal retention and zero demonstrated write rate, a medium with dynamical states and no demonstrated pen, which on the computed lattice pins the record axis to the fermionic register. The survey is a characterization, not a derivation: nothing here selects the home cell dynamically, and no anthropic claim is made.