Thank you very much for the thorough and generally positive feedback. R1.1 However, I worry about the reproducibility since most of the results are run by only once. F or the equation between line 135 and 136( why does it not have a equation number?): We will add an equation number. The experiments stops on L=20.

Large Language Models (LLMs) demonstrate complex responses to threat-based manipulations, revealing both vulnerabilities and unexpected performance enhancement opportunities. This study presents a comprehensive analysis of 3,390 experimental responses from three major LLMs (Claude, GPT-4, Gemini) across 10 task domains under 6 threat conditions. We introduce a novel threat taxonomy and multi-metric evaluation framework to quantify both negative manipulation effects and positive performance improvements. Results reveal systematic vulnerabilities, with policy evaluation showing the highest metric significance rates under role-based threats, alongside substantial performance enhancements in numerous cases with effect sizes up to +1336%. Statistical analysis indicates systematic certainty manipulation (pFDR < 0.0001) and significant improvements in analytical depth and response quality. These findings have dual implications for AI safety and practical prompt engineering in high-stakes applications.