Why Abiogenesis Experiments Produce Building Blocks But Not Codes: An Effective Dimensionality Threshold

Seventy years of abiogenesis research have produced amino acids, nucleotides, lipid vesicles, and ribozymes — but no codes. Why?

Mathematical foundation: The Fisher rank increase under coupling is proven rigorously in Manifold Expansion via Coupling, which provides the formal basis for why D_eff > 1 enables code emergence.

Code emergence requires sufficient effective dimensionality (D_eff) — not merely many chemical species, but species whose dynamics span orthogonal information channels. We demonstrate a threshold at D_eff > 1: collapsed dynamics achieve >80% accuracy in only 35% of cases, while diverse dynamics achieve it in 71%.

The mechanism is substrate competition: competitive binding for shared resources discretizes continuous chemical gradients into stable boundary codes. Crucially, graded competition works as well as cooperative binding — what matters is competitive allocation, not winner-take-most amplification.

The formose reaction, with autocatalytic structure creating divergent dynamics, may approach code-emergence conditions.