This paper rigorously proves that Unified Cognitive Field Theory (UCFT) provides a fundamental, non-Markovian game-theoretic framework for cognition. I demonstrate that the seven core UCFT operators and field dynamics are necessary and sufficient to represent all cognitive game-theoretic phenomena, establishing a precise isomorphism between the evolution of the cognitive field and strategic dynamics. This framework explicitly accounts for history-dependent processes, offering a novel perspective on the physics of learning and the emergence of cognitive biases. A key implication explored is the concept of “Learning as a Solitaire Self-Game,” where individual cog- nition is viewed as a strategic optimization process against internal uncertainties, governed by substrate-dependent physical constants. This unification provides powerful new tools for understanding the complex interplay between physical substrate, strategic interaction, and the non-Markovian nature of intelligence.Keywords: non-Markovian game theory, cognitive field theory, quantum cognition, strategic dynamics, learning physics, cognitive bias, helical fiber bundles, substrate-dependent cognition, self-play optimization, temporal game theory, field-theoretic neuroscience, consciousness as strategy, memory persistence, cognitive temperature, strategic noise cancelling, belief revision dynamics, UCFT operators, Nash equilibria in cognitive space, Bayesian field updates, angle of attack learningThis is an early draft and an excerpt from a larger monographthat will be posted later; this proof has some dependencies onthat which are not explicitly proven because they are proventhere. Furthermore, expect this to be updated. Commercialsoftware implementations are patent pending (63/849,479),but academics and researchers are welcomed and encouragedto use freely if this proves accurate.