Ambiguity-Aware Multi-State Computation in State-Aware Graph Systems

Modern computational systems are commonly designed around deterministic or discrete state-based models, where uncertainty is typically resolved early during state evaluation. [1], [14], [22] The framework further distinguishes deterministic Absolute States represented as {Abs}_A = (-1, 0, +1) and equivalently expressed as |A| = (-1, 0, +1) from derived ambiguity-preserving Q-States, enabling state-aware evaluation without forcing immediate collapse into rigid binary interpretation. [A:Absolute State]. However, many real-world systems operate under conditions where ambiguity persists, evolves, and directly influences system behavior [A1:Ambiguity]. This paper introduces an ambiguity-aware computation method operating within a Multi-State Computational Model, where Q-States are treated as a first-class computational state construct [A2:Q-State]. Instead of forcing immediate resolution, the proposed computational method preserves, interprets, and propagates ambiguity through a structured Transformation Pipeline. The pipeline integrates State Derivation, Q-State Identification, and State-Aware Graph Evaluation. [A3:State-Aware]. A key conceptual distinction is established between Computing State and Computational State, enabling ambiguity-aware evaluation under structured operational constraints. [A4:Computing vs Computational State]. The proposed computational methods incorporate Lattice-Based Representation and Node State Classification to model system behavior under ambiguity [A5:Node-State]. Sparsity Dynamics and Path Validity are introduced as core evaluation mechanisms, supported by Boundary Conditions and Hysteresis Dynamics to maintain stability, continuity, and evaluation consistency [A6:Sparsity, Path-Validity]. Simulation results demonstrate controlled Q-State propagation and convergence toward high Confidence Interval (CI) outcomes under structured ambiguity constraints [A7:Boundary-Conditioned Hysteresis]. This approach provides a foundation for modeling complex systems where uncertainty is not prematurely eliminated, but systematically represented, evaluated, and incorporated into state-aware computational evaluation. [A8:Graph-Based Systems].