Nick Lane's hypothesis proposes that life originated not from a prebiotic soup but from the geochemistry of alkaline hydrothermal vents. Where hydrogen-rich fluids from serpentinizing rock met CO₂-laden ocean water, a natural electrochemical gradient drove carbon fixation — the same reaction that powers the acetyl-CoA pathway in modern methanogens and acetogens.

This playground models a threshold question: molecules are randomly assigned roles (A, C, B) and distributed across vent pore compartments. Each compartment is checked for a Lane-like motif. The central parameter is catalytic density λ — the probability that any given molecular interaction actually catalyzes a reaction.

The threshold N* marks where P(H_L) crosses the target probability. Empirically, N* scales with λ as a power law. The heuristic analysis predicts:

Compartmentalization matters: vent pores act as natural reaction vessels. More pores (higher q) dilute molecules across compartments, pushing thresholds upward. But each pore provides an independent trial — a tradeoff between concentration and combinatorial opportunity.

This is a toy model — no stoichiometry, kinetics, or thermodynamics. It captures threshold behavior, not chemistry. The point is that the transition from "possible" to "nearly forced" can be sharp, and that sharpness does not depend on any one lucky compartment but on the statistics of the entire vent system.