Emergent matter · structure

What phase of matter does an emergent Particle Life world form — a gas, a liquid, or a crystal?

How the lab tests it

Measure the pair-correlation function g(r) — the radial distribution function from statistical mechanics — by time-averaging a toroidal histogram of every pairwise separation over the live field, normalised so g = 1 means 'as likely as random'.

What it looks for

the g(r) shape: flat g ≈ 1 (gas), a first peak with damped oscillations (liquid, short-range order), or many sharp peaks (crystal). A first peak far above ~3 signals two-phase coexistence (dense droplets in gas), since g(r) is normalised by the global density