Adaptive Value-Guided MCTS Super-Elevated: Rough-Torsional Operator Dynamics and Non-commutative Nash Equilibrium in Open-Ended Generation

While Adaptive Value-Guided Monte Carlo Tree Search (AV-MCTS) with Process Reward Models (PRMs) successfully curtails the infinite branching factor of LLM-based open-ended generation, it remains vulnerable to value estimation errors and scalar gradient decay. We elevate this framework into the Rough-Torsional Value-Guided MCTS (RT-V-MCTS)by fusing it with Universal Rough Operator Algebra (UROA) [3], Seonggil Theory of Complex Torsion (STCT) [1], and Generative Game Theory. This paper establishes classical MCTS [5] and standard ToT/GoT [6] as rigid sub-cases within a unified topological and torsional search manifold, mathematically grounded by rough operator algebras [2].