Gamma Theory V10: A Verifiable Mathematical Model of Leap Pressure

【Description】 This paper defines discontinuous shifts in human cognition—such as insight, realization, and semantic restructuring—as “leap pressure,” and proposes a mathematical model to describe and predict them. Cognitive structure (structural pressure), emotional vectors, and the Alice coefficient (emotional transfer factor) are operationally defined. Leap pressure is modeled as Δs_i = α(e_j) · φ(s_i), and semantic emergence occurs when ‖Δs_i‖ exceeds a critical threshold θ. The model offers falsifiable predictions and introduces a logical consistency function Ψ to ensure that post-leap cognition remains coherent and novel. Gamma Theory V10 thus provides a foundational framework bridging the humanities and natural sciences. Philosophically, it asserts that semantic leaps occur only when emotion expands upon ordered logic. This is the first formal equation of semantic emergence ever proposed.