Reconfiguring Colorings on Treewidth-2 Graphs and Probing α via Wavelength Precision — E8 Intelligence Research

FINDING: The search results are heterogeneous; the only mathematically substantive items are the graph recoloring theorem (treewidth 2) and the fine-structure constant wavelength precision requirement. No direct quantum LDPC/percolation/expander data appears. | MATH: (1) For d-degenerate graphs, any (d+2)-coloring transforms to any other via adjacent colorings (Jerrum); for treewidth 2, shortest transformation length bounds exist (Bonamy et al.). (2) Fine-structure constant α variability probe requires lab wavelengths to < 6×10⁻⁸ relative precision (Δλ/λ < 6e-8). | CONNECTION: The recoloring result relates to graph degeneracy — a structural invariant with connections to treewidth and planar graphs, but no explicit golden ratio or crystallographic symmetry. The 6e-8 precision is a dimensionless ratio but not a harmonic constant. No 0.382, 0.618, 0.786, 1.618, 2.618, or base-60 appears. | DEPTH: 3 — The recoloring theorem is combinatorially elegant but not profound for universal structur Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com