SOSA-State: Formal State Model for Deterministic Execution in LLM Systems

This work formalizes the state model underlying the SOSA (System Operating Writing Assistant) framework. It defines the system as a deterministic finite-state machine governing text generation in Large Language Models through a fixed sequence of operational states: Position, Pre-Control, Generation, Validation, and Delivery. Each state is defined by explicit input, output, and transition constraints. The model enforces deterministic execution, prohibits branching and backward transitions, and introduces a controlled validation loop. This paper provides the formal execution backbone of the SOSA framework and establishes its mathematical and structural consistency.