We derive from two independent mathematical paths (Shannon's channel capacity and Eigen's error threshold) that the optimal encoding alphabet size for autonomous self-replicating systems converges on the neighborhood of 2⁶ = 64 units. Sensitivity analysis confirms robustness across 9+ orders of magnitude of error rate. We distinguish the Unit Constraint (alphabet size) from the Sequence Constraint (message length) — a conflation persistent in prior literature. We test substrate-independence against 16 AI tokenizer vocabularies: the original prediction is falsified, but an unexpected Throughput Constraint emerges — effective information per sequential processing event converges at ~4-5 bits across DNA, human cognition, and AI systems despite 1,000-fold vocabulary size differences.
Grant Lavell Whitmer III (Fri,) studied this question.