Strategic Taxonomy in Heterogeneous Landscapes: Dynamics of Topological Collapse and Convexity Detection

Classical game theory often assumes static payoff matrices. This paper proposes a dynamic framework for "Heterogeneous Landscapes," where the topological class of a game (Zero-Sum, Negative-Sum, Positive-Sum) is mutable based on agent behavior and trust decay. We formalize the Trust Parameter τ (t) as a state variable governed by differential dynamics and derive the critical threshold τ c , below which Positive-Sum systems irreversibly collapse into Negative-Sum "Pyrrhic Traps." Furthermore, we formalize the "Mustard Seed" phenomenon as a Signal Extraction Problem, distinguishing between observers optimizing for current state variance (Type S) and those detecting latent convexity (Type V). We present the Loyalty Filter Algorithm, provide bounds on recovery versus decay, and validate the topological collapse via agent-based simulations.