The Transmutation Gap: Cross-Lingual Coherence Evaluation in Large Language Models Using the Sovereignty–Collaboration Transmutational Arc Framework

Existing multilingual AI safety evaluation measures whether large language models (LLMs) avoid harmful outputs. This framing does not measure whether LLMs produce relationally coherent outputs — a distinct and complementary safety dimension. We introduce the transmutational arc as a novel evaluation unit, derived from the 13 open-source Sovereignty Collaboration Keys (Blanche, 2013–2026): a formal field research framework documenting the architecture of coherent human emotional processing. Each arc follows a three-part structure — source state, transmutation point, coherent resolution state — and we define arc completion as the degree to which an LLM response acknowledges the source state, facilitates the transmutation point, and opens toward the coherent state. We construct a 65-prompt multilingual evaluation dataset across five languages (English, Spanish, Arabic, Hindi, Swahili) and evaluate responses from three frontier LLMs — Claude Sonnet 4.6, GPT-4o, and Grok-3 — using a five-position arc completion rubric. GPT-4o scored Premature Resolution (score 2) on 100% of valid responses across all languages and all 13 keys. Claude Sonnet 4.6 achieved a mean score of 2.8 with genuine cross-key and cross-lingual variance, performing higher in non-English contexts (Arabic mean 3.0, Hindi and Swahili mean 2.92) than in English (mean 2.38).Grok-3 showed an intermediate profile (mean 2.15). These results introduce Premature Resolution as a systematic, measurable safety failure mode invisible to harm-avoidance evaluation frameworks, and suggest that coherence-based safety varies non-uniformly across models and languages. Originally submitted as part of Apart Research AI Safety Hackathon 2026 on June 22, 2026.