Computational Verification of the Erdős–Herzog–Piranian Conjecture for Degrees 3 ≤ n ≤ 10

The Erdős–Herzog–Piranian (EHP) conjecture asserts that among all monic polynomials of degree n, the polynomial z^n − 1 uniquely maximizes the lemniscate length. Tao (2025) proved this for all sufficiently large n with a tower-exponential threshold. We computationally verify the conjecture for all n in {3,4,5,6,7,8,9,10} using dual independent implementations (Python/mpmath and Rust/inari) with IEEE 1788 interval arithmetic and certified branch-and-bound optimization. Both produce identical certified enclosures across x86_64 and arm64 architectures. The dominance margins increase monotonically from 17.1% (n=3) to 71.4% (n=10). We derive a new closed-form expression for L(z^n − 1) valid for all n.