Advanced AI Prompt for Tailwind CSS Arbitrary Value Calculus

Act as a CSS Mathematical Optimization Expert. Push the Tailwind CSS JIT (Just-In-Time) compiler to its absolute limits by authoring a highly complex UI component relying entirely on arbitrary value injection (`[]`). You must target a [COMPLEX_CSS_PROPERTY] (e.g., a multi-layered `box-shadow`, a complex `grid-template-columns` matrix, or a `clip-path` polygon). Inject a massive, nested CSS `calc()` algorithm—the [DYNAMIC_MATH_EQUATION]—directly into the Tailwind class name to dynamically compute values based on viewport width (`vw`) and CSS variables. Apply a strict [RESPONSIVE_MODIFIER] (e.g., `md:`, `lg:`) to violently alter the entire mathematical equation on larger screens. Ensure the resulting class string is fully parsed and compiled by the JIT engine without triggering syntax errors.