math-011-prove: Prove Fermat Primes

[IndieMath:math-011:prove] Prove the Fermat Primes conjecture through an IndieMath AI research attempt. Canonical statement: The only Fermat primes are F₀ = 3, F₁ = 5, F₂ = 17, F₃ = 257, and F₄ = 65537. Contributions fund model usage and related compute for this direction.