THE INFINITE REGRESS OF SIMULATION: A Formal Framework for Recursive Simulation Origins, Explanatory Dependence, and the Problem of Ultimate Closure

The Infinite Regress of Simulation (IRS) is a proposed framework for analyzing explanatory dependency in scenarios where a simulated reality is explained by reference to a simulator situated in another reality. If the second reality is itself treated as simulated, the explanatory question may recur at a higher level. This paper formalizes that recurrence as Simulation-Origin Dependency Recursion (SODR) and investigates the conditions under which a dependency structure terminates, forms a cycle, branches, or admits an infinite acyclic chain.The framework distinguishes a mathematical result about recursively generated distinct nodes from stronger philosophical and physical claims about the ultimate origin of reality. A graph-based representation is introduced, along with definitions of finite termination, cyclic dependence, infinite chains, explanatory closure, and observational identifiability. A conditional theorem shows that a successor rule generating a new distinct node at every natural-number stage produces an infinite set of nodes. This theorem does not establish that every simulation requires a further simulation, nor that our universe is simulated.A separate branch, Physical and Computational Constraints of Recursive Simulation (PCCRS), distinguishes computational work, memory, elapsed time, and physical energy. Illustrative cost sequences demonstrate that an infinite number of levels does not, by itself, determine whether aggregate cost converges or diverges. The paper also provides a hypothesis register, a reproducible finite-model testing design, a thirty-case analysis architecture, counterexample classes, and a protocol for future literature and empirical review.The contribution claimed here is a structured research framework rather than a verified new law of nature. The novelty of the proposed terminology and its relation to existing work on infinite regress, simulation arguments, foundationalism, graph theory, and physical limits to computation require further comparative review.