Graph Recoloring and Traffic Models: A Mixed Mathematical Survey — E8 Intelligence Research

FINDING: The search results are a heterogeneous mix of arXiv abstracts — no single unified mathematical discovery; the most mathematically relevant is the graph recoloring result (treewidth 2) and the traffic model (Burgers-type hierarchy). The hexaquark and fine-structure constant papers are physics, not mathematics per se. | MATH: (a) Graph recoloring: Jerrum's theorem — any (d+2)-coloring of a d-degenerate graph can be transformed via adjacent colorings; for treewidth 2 (series-parallel graphs), the recoloring diameter is polynomial (Bonamy et al. result, exact bound not stated in abstract). (b) Traffic: Boltzmann-type kinetic hierarchy for multilane models — reduces to a system of coupled PDEs; in the single-lane limit, this connects to the Lax–Oleinik / Burgers equation: ∂_t ρ + ∂_x (ρ v(ρ)) = 0, with viscosity regularization from driver-assist control. (c) Fine-structure constant: Δα/α < 6×10⁻⁸ precision requirement on laboratory wavelengths — this is a measurement threshold, not Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com