Morphic Resonance as a Topological Phase

Morphic resonance—the hypothesis that formative influences persist across time and space, making patterns of organization more likely to recur the more often they have occurred—lacks a formal physical model. This paper proposes that morphic resonance can be understood as the evolution of a topological phase in the state-space of a complex system. We build upon a foundational model where stable morphologies are represented as eigen-configurations (attractors) of an underlying causal graph, characterized by a Morphogenetic Potential, U. We then introduce a critical dynamic extension: the graph itself evolves via a History Tensor, H(t), which encodes the system's past states. This results in a time-modulated potential, U(s,t) = U₀(s) exp(-αH(s,t)), where recursive historical instantiations deepen the attractor basins of specific eigen-forms. This formalism translates "habit" into mathematics, predicting hysteresis, increased stability, and decreased convergence time for repeated forms. We thereby reframe morphic resonance not as a mysterious force, but as the natural consequence of a system whose topological landscape of possible forms is recursively shaped by its own history.