Many infinite clusters: percolation in hyperbolic space (3D)

About this app

A dome of heptagons, the {7,3} lattice of the hyperbolic plane: every edge is open with probability p. Between p_c and p_u several separate clusters reach the rim at once; on ℤ² it jumps straight from none to one. Dome, Poincaré disc and ℤ² comparison, counter and curve over p. Benjamini–Schramm 1996, proved for every nonamenable graph in openai/math, family 214 (formalised in Lean). Exhibit-ready.

Subject: Open problems, solved by AI

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