4 papers
Unified Nilpotent Operational Framework: Foundations, Algebraic Exactness, and Complexity
Ramon Moya
A unified algebraic framework is developed to study nilpotency as a structural mechanism for exactness in operational, combinatorial, and computational problems. The central object…
Vector Determinant in the ARE Framework: From Scalar to Vector-Valued
Ramon Moya
The ARE (Action, Rectification, and Structure) method is presented as a framework for reorganizing the Leibniz expansion of the determinant through the action of the cyclic group C…
ARE Method: Orbital Decompositions and Dihedral Cancellations for Determinants
Ramon Moya
We develop the ARE method (Action-Rectification-Expansion), a structural framework for the organization of Leibniz terms in determinants through cyclic group actions and orbital de…
Exact Nilpotent Collapse of Born-Neumann Expansions in Finite Quantum Systems: A SON Formulation for Exact Algebraic Closures of Scattering Series
Ramon Moya
We identify a class of finite quantum systems, namely, acyclic systems whose transition graph is a directed acyclic graph (DAG), for which the Born series collapses into an exact a…