First computational upper bound on the infimum for Erdős Problem #1038

v2.0 update: Added Thomson/Riesz energy mapping and stability analysis of the extremal configuration.

Main result (v1): inf ≤ 1.837 (N=200 configuration) for the sublevel set measure |{x ∈ ℝ : |f(x)| < 1}| of monic polynomials with all real roots in [-1,1].

New in v2 — Energy mapping: The log-energy minimizer (Saff-Totik weighted potential theory) reproduces the extremal atom weight within 2.1% (0.809 vs 0.826), demonstrating that the atom+cloud architecture is a structural feature of the problem geometry, not a numerical artifact.

New in v2 — Stability analysis: The extremal configuration sits in a single convex basin with positive-definite Hessian (det = 1726). The basin is highly anisotropic: 35× stiffer in atom weight than cloud width. No secondary local optima detected.

New in v2 — Cloud-potential displacement: The extremal cloud sits 0.343 units left of the Saff-Totik equilibrium point, quantifying the cost-function difference between sublevel minimization and weighted energy minimization.

Conjecture: The exact infimum equals 11/6 ≈ 1.8333.

AI Disclosure

Computations implemented and executed with Claude (Anthropic). Experiment design, analysis, and interpretation assisted by Claude. All numerical results are independently reproducible from the provided source code and data files.