Abel's Revenge: The Death of P = NP

In 1824, Niels Henrik Abel proved that polynomial equations of degree five and higher cannot be solved by radicals. The obstruction is the alternating group A₅ - the smallest non-abelian simple group, admitting no decomposition into smaller factors. This paper establishes that the same algebraic obstruction governs computational complexity. I introduce the Computational Galois Group - an invariant capturing the symmetry structure of solution spaces - and demonstrate that NP-complete problems in the frozen phase encode A₅ as a composition factor. This encoding activates two independent barriers: The Overlap Gap Property (OGP): defeats all algorithms navigating by gradients, correlations, and local information…