# Verification report

The manuscript proves finiteness of nonexceptional equilibria for rational inverse-power fields in every dimension. It includes all same-sign equilibria, without genericity or nondegeneracy assumptions.

The proof is a self-audited extension of the compact-curve method of Enciso and Peralta-Salas. The extension replaces their dimension-three step with a scalar projection and handles rational exponents through finite algebraic root coordinates. Every physical lift is proved isolated in the complex algebraic system before a degree bound is applied.

The included standard-library checker tests finite-site order inequalities, exact scalar projections, denominator clearing, and the two explicit failure cases outside the theorem's hypotheses. It uses rational arithmetic and does not constitute a formal proof of the general theorem.

The original question and the recent prior theorem were checked in their primary sources. The three-dimensional Coulomb result is credited as prior work. No claim of absolute novelty, independent refereeing, or machine formalization is made. Third-party source PDFs are not redistributed.

The author appears alone in the title block, with affiliation and contact in a footnote. AI assistance is disclosed in a prose paragraph, not as a separate section.