From Roundoff to Heredity: Finite-precision exposure can produce inherited reproductive failure and selection in digital life

Preprint. Finite-precision arithmetic is usually treated as implementation error. In a self-reproducing computation, however, a bounded rounding exposure may alter an offspring and enter the causal chain of heredity. We tested five successive rungs: numerical divergence, persistence after return to baseline float32, transmission through native reproduction, inherited functional change, and selection under limited population capacity. Software quantization was the causal intervention; exact p24 shams, held-out founders, common-garden propagation, injection/rescue, and deterministic replay separated inherited effects from trajectory divergence. In a neural cellular automaton, one p8 exposure produced later reproductive failure in 21/36 and 10/36 founders under two of three rules, versus 0/108 matched p24 shams. The exposed parent had to reproduce before daughter extraction, and descendants then propagated under ordinary float32 without further p8 treatment. An identical-offspring comparison did not meet its frozen family-level amplification criterion when p8 was reapplied during descendant reproduction, despite a near-threshold increase in one rule. Exact paired comparisons remained significant after correction, and the affected ancestries subsequently declined under finite-slot competition. In two external codebases developed independently of this study, Flow-Lenia showed persistent change without validated heredity, whereas Google's published self-replicating neural agents transmitted impaired copy function through eight post-exposure baseline-float32 generations and showed model-specific ancestry loss. Gray-Scott also expressed inherited functional effects, while Lenia largely buffered severe rounding. Controlled rounding can therefore generate transmitted, inherited functional variation that selection can act against. Its expression depends on substrate, rule, precision, rounding operator, and ecological bottleneck. We found no beneficial adaptation, open-ended evolution, or independent-investigator replication. The separately archived reproducibility package is publicly available at DOI 10.5281/zenodo.22685612.