Boggavarapu, K.

Biological inheritance can be treated as a class of catalytic templating reactions in which a daughter molecule, generated by a kinetic kernel acting on a parent template, is itself a substrate for the next round of the same catalysis. We give the physicochemical conditions under which such a reaction can support unbounded heritable molecular distinguishability. Four conditions on the template-operator pair organize the analysis: nonzero per-site information content under the active-site recognition kernel (R1), a count of independently variable recognized positions that grows without bound as the reaction extends (R2), catalytic closure under iteration, possibly through a reversible involution such as Watson-Crick complementation (R3), and stochastic drift of the kernel in its recognition alphabet (R4). A fifth, scope-defining condition (R5) restricts the principle to kernels that are intrinsic physicochemistry rather than externally optimized search. These conditions are necessary for two distinct outcomes, separable as two necessity results. The capacity theorem states that linear scaling of substrate Shannon capacity with reaction extent requires R1, R2, and R3 but not R4: a perfect copier transmits an exponentially large configurational ensemble while producing no novelty. The generation theorem states that diversification of the heritable configuration set beyond the deterministic closure of a finite initial repertoire additionally requires R4, because branching trajectories in the recognized alphabet are what produce innovation. Population-level kinetics follow as a corollary that organizes six attested templating reactions into a taxonomy, and as a finite-population, finite-horizon proposition tested over five inheritance kinetic schemes, in which only individual-level stochastic drift reaches the target within the model class. We test the framework on the recently characterized bacterial defense system Drt3b, which makes alternating poly(AC) DNA without using a nucleic acid template. The framework classifies Drt3b as a cyclic two-state catalytic templating channel with a 1-bit capacity ceiling, and predicts that the Glu26-to-Gln active-site mutant incorporates {Delta}G at 10% probability at the {Delta}A-selecting state; the published biochemistry reports 10.16%. Across 1,232 Drt3b homologs, the framework predicts and recovers a 15.7-fold elevation of {Delta}G misincorporation in six clades carrying the natural Glu26-to-Asp substitution at this gate. Substitutions at two universal gate residues, Arg253 (architectural) and Gly248 (selectivity), provide single-experiment site-directed mutagenesis tests of the framework's predictions.