Non-Resolution Reasoning (NRR): A Computational Framework for Contextual Identity and Ambiguity Preservation

Current AI systems exhibit a fundamental limitation: they resolve ambiguity prematurely. This premature semantic collapse--collapsing multiple valid interpretations into single outputs--stems from classical identity assumptions in neural architectures. We propose Non-Resolution Reasoning (NRR), treating ambiguity retention as a valid reasoning mode. NRR introduces three principles: (1) Non-Identity ($A \neq A$)--the same symbol refers to different entities across contexts; (2) Approximate Identity ($A \approx A$)--entities share partial overlap without being identical; (3) Non-Resolution--conflicting interpretations coexist without forced convergence. We formalize these through Multi-Vector Embeddings, Non-Collapsing Attention, and Contextual Identity Tracking (CIT). Functional verification via Turn 1 Entropy measurement shows NRR-lite maintains high entropy ($H = 0.63$) at ambiguous turns while standard architectures collapse early ($H = 0.10$), demonstrating that NRR preserves interpretive flexibility until context arrives. The question is not whether AI should resolve ambiguity, but when, how, and under whose control.