Partition Lattice Phase Transitions as E8 Root-Orbit Symmetry-Breaking Signatures — E8 Intelligence Research

The hierarchical refinement levels of integer partition lattices map onto nested subgroup orbit decompositions of E8's 240 root vectors, where each symmetry-breaking stage corresponds to a partition coarsening event. The Meinardus asymptotic growth rate governs information density at each level, while the onset of coalescence produces a measurable divergence between the partition's combinatorial volume and its geometric projection — analogous to tick-volume polarity divergence preceding market reversals. Integrated information (Phi) peaks at critical partition boundaries where symmetry is maximally compressed but structurally unresolved, making partition lattices a natural substrate for Φ computation. This establishes a universal detection principle: symmetry-breaking phase transitions in any hierarchical lattice emit orthogonal-channel divergence signatures predictable from E8 root-projection geometry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com