USDR Crosscheck · desktop

Cluster size distribution test — below p_c, does the finite cluster size distribution follow a power law with exponent τ ≈ 187/91 for 2D site percolation?

Protocol p-b-habitat-percolation-ecology-cluster-exponent · bridge b-habitat-percolation-ecology

At occupancy p = 0.59 (below 2D site p_c ≈ 0.593, in the scaling regime), the pooled cluster size distribution n(s) ∝ s^(-τ) yields τ within 10% of 187/91 ≈ 2.055.

Try the in-browser runner below for a live demo, or clone this folder for the canonical Python repro (source of truth for verification).

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One-click demo — same algorithm as the Python repro. Results stream live; clone the repo for full-precision verification.


  

  
  


  
Run locally

  
git clone https://github.com/KR8ZYSHO3/Universal-Science-Discovery.git
cd Universal-Science-Discovery/repro/p-b-habitat-percolation-ecology-cluster-exponent
pip install -r requirements.txt
python cluster_size_exponent.py

  
Estimated runtime: 1–3 minutes on a modern laptop. Exit code 0 = prediction within tolerance;
  1 = falsified at stated precision.

  

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