I have identified a hypergraph rewriting rule that matches the Wolfram Physics Project's search criteria for fundamental physics.

The Rule:

· Base graph: Regular hexagonal tiling (A₂ lattice) · Vertex degree: 3 (each vertex connects to 3 neighbors) · Invariant: κ = P/D = 3 (perimeter/diameter ratio derived from honeycomb conjecture) · Rewriting operation: At each coarse-graining step, replace each hexagon with a single vertex at scale factor 3

What this rule produces:

1. Scale ladder Lₙ = ℓ_p × 3ⁿ
2. Particle masses M = v_EW (n/27)^{1/d} with n = a²+ab+b²
3. Fine structure constant α⁻¹ = 137 + 12/φ¹²
4. Gravity emerges from information stress-energy tensor as κ → π

Pre-registered paper: viXra:2512.0067

Attachments:

Entropic_Ladder_...docx