Causal Emergence of Signature-like Phase Separation in Coherence-Constrained Networks

We demonstrate that constraint networks with a coherence-protection mechanism exhibit a structurally inevitable phase separation between two edge populations with qualitatively distinct symmetry properties — one symmetric (proto-spatial), one direction-broken (proto-temporal). Using a 2×2 factorial design, we establish that this separation requires both local cohesive structure (triangles) and a coherence-protection term — neither alone suffices (F (1, 96) = 4497, p < 10⁻⁶⁰). A bifurcation theorem proves the result holds for any convex, even penalty function with positive curvature at the origin. Dynamic stability analysis confirms a unique attractor basin robust to large perturbations. All scripts and data are available at https: //github. com/zeekmartin/tcge-code/tree/main/causalcontrols This article presents a self-contained result from the TCGE programme (Theory of Emergent Global Constraints). The full framework is described in a companion preprint: doi: 10. 5281/zenodo. 18297823 Methodology note: Mathematical formalization and computational implementation were developed in collaboration with AI systems (Claude, Anthropic). The author maintains full conceptual direction and responsibility for all scientific claims.