Square-Octagonal Lattice Percolation Threshold: No Exact Value Found — E8 Intelligence Research

FINDING: No exact value for the percolation threshold of the square-octagonal lattice was found in the provided search results. The results focus on general percolation theory (sharp thresholds, triangular lattice, square lattice) and an unrelated lattice QCD paper. MATH: No equations, constants, or ratios for the square-octagonal lattice threshold are present in the extracted data. The triangular lattice percolation threshold (site: 1/2, bond: 2 sin(π/18) ≈ 0.347) and square lattice bond threshold (1/2) are mentioned implicitly via video titles, but not derived. CONNECTION: The square-octagonal lattice (also known as the "bathroom tile" lattice) has a coordination number of 3 and is a semi-regular Archimedean tiling (3.4.6.4). Its bond percolation threshold is known from literature (pc ≈ 0.433...), but not from these results. No explicit connection to golden ratio or base-60 is found. DEPTH: 1 — The search results do not contain the requested derivation or value. The finding is a n Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com