Finite-count chemical inheritance with reversible interactions and bounded food supplies

We construct a finite stochastic chemical system that transmits four labels, encoded in the normalized composition of its resident molecules, through a complete growth-and-division cycle with an explicit uniform probability. Two modules interact through reversible cross-catalytic channels with strictly positive rates in both directions. Each module conserves its resident-plus-food molecule count during a closed reaction batch; the only external operations are a scheduled fair split of every molecule and a label-blind food replenishment that reads module totals. With nine modelled molecules per module, every admitted newborn contains at most sixteen residents and each compartment holds eighteen residents plus food. Uniformly over all admitted states and all four labels, the probability that both complementary daughters return to the admitted region of the same label by time twenty is at least $8046297159/8112104000>0.99188782$; with twenty molecules per module the bound is $0.99998459$. The guarantee stays above $0.99025694$ on an explicit three-parameter box around the nominal rates. The proof uses an empty-daughter observable that equals the fair-partition failure probability exactly, together with a finite-state generator inequality, and its constants are within $2.5\times10^{-4}$ of the numerically evaluated one-cycle probability. Within the stated pure-species, two-module, fair-allocation architecture, eighteen peak residents are necessary and sufficient for a $99\%$ guarantee. We also prove a sharp normalized-composition separation of $2/K$, two-sided bounds for a selected lineage and for a complete binary family of descendants, and an exact product-form stationary law. The uniform probability bound, the identification of the count chain with the literal twenty-four-channel chemistry, and the composition geometry are verified in Lean 4; the structural consequences are proved conventionally and are identified as such. The labels occupy disjoint species supports, the mechanism is an amplification-and-partition guarantee rather than multistability, and it has no defence against contamination by an absent species.