ABELIAN SANDPILE — IDENTITY

Abelian sandpile group: Each stable config c (with 0≤c_v≤3 for Z²) is an element. The group identity is the unique stable config e such that e+e stabilizes to e.

The identity has fractal self-similar structure — a purely emergent algebraic phenomenon.

Topple rule: If c_v ≥ 4, fire: c_v−=4, neighbors +=1. Iterate until stable.