How do individual value orientations give rise to collective evaluative structures, and can such emergence illuminate concepts from process theology? This paper addresses both questions through a formal axiom system and its application to non-personal conceptions of the divine. We introduce C5, an axiom system for "coherence-capable agents"—entities that orient toward structural consistency in their evaluations. Drawing on Thagard's (1989) constraint-satisfaction model, we formalize coherence as a bilinear functional over relational structures. The framework includes a distortion operator modeling how agents can act contrary to their coherence-seeking orientation, and an aggregation mechanism that sidesteps Arrow's impossibility theorem by stipulating weights rather than deriving them from ordinal preferences. Our central result characterizes when aggregated value structures are weakly emergent in Bedau's (1997) sense: ontologically reducible but epistemically non-trivial, resisting decomposition into sums of individual contributions. The global positive attractor exhibits precisely this non-additive character. As application, we develop a structural mapping between this framework and process philosophy. Whitehead's "consequent nature" and Spinoza's Deus sive Natura admit reconstruction as emergent coherence attractors. We analyze which theological traditions align: process theology and Spinozism fit naturally; classical theism does not. This proposal offers conceptual clarification, not metaphysical proof. The framework provides precise vocabulary for articulating what process theologians mean by "emergent" God-concepts, enabling rigorous interdisciplinary dialogue.