Large language models routinely operate in environments where authority is contested, identities overlap, and probabilistic inference preserves multiple plausible readings without determining which distinctions should govern analysis or action. This paper reports empirical evidence that explicit significance weighting, formalized as an S-vector with dimensions for identity stability (Sr), operational consequence (Sc), and temporal relevance (Su) (among others) produces systematic and convergent effects on reasoning behavior across architecturally distinct language model systems. We tested significance-guided reasoning using structured scenarios requiring resolution of contested authority where inference proved insufficient. Testing covered two system classes: four frontier conversational models and three retrieval-augmented generation systems (OpenAI GPT-5.2, Google Gemini 3.0, Anthropic Claude Sonnet 4.5, xAI Grok 4.1, NotebookLM, Claude Projects, Perplexity). All systems were evaluated under controlled conditions comparing inference-only responses with significance-weighted responses using identical scenario content. Where reasoning traces were available, S-vector application reduced reasoning effort by 40-60% while improving completion rates. In retrieval-augmented systems, significance weighting addressed a distinct failure mode: not knowledge insufficiency, but domain collision among equally well-sourced competing truths. All three RAG systems produced identical priority orderings under significance criteria that they could not generate through inference alone, demonstrating that the framework enables principle-based resolution of cross-domain authority conflicts without narrative synthesis or institutional defaulting. All seven systems tested, spanning two architectural classes and four organizations, converged on identical operational priority orderings under significance criteria, a consensus none could generate through inference or retrieval alone. These findings establish behavioral validity for significance weighting as a governance mechanism for semantic ambiguity in large language models. The observed effects emerged at the prompt level without architectural modification, suggesting immediate production applicability, while validating the theoretical framework for deeper integration. The results position significance weighting as a missing control layer in contemporary language model systems, one that becomes essential as retrieval breadth expands and operational deployment requires resolution of contested claims under conditions of genuine ambiguity.