Function judge

benchmarks/audit/solve.ts:158–175

(
  c: Case,
  returned: number,
  sound: number[],
  badReal: number
)

/** Grade a Wolfram batch result with the same soundness+completeness oracle as
 *  CE: a returned real root is sound iff |residual| < TOL. */
function gradeWolfram(c: Case, res: any): { v: Verdict; note?: string } {
  if (!res || res.status === 'error') return { v: 'error', note: res?.error };
  if (res.status === 'timeout') return { v: 'error', note: 'timeout' };
  const roots: any[] = res.roots || [];
  const mags: any[] = res.values || [];
  if (res.status !== 'ok' || roots.length === 0)
    return { v: c.verify.cardinality === 'empty' ? 'correct' : 'unsolved' };
  const sound: number[] = [];
  let badReal = 0;
  for (let i = 0; i < roots.length; i++) {
    const rv = Number(roots[i]);
    if (!isFinite(rv)) continue;
    const m = Number(mags[i]);
    if (isFinite(m) && m < TOL) sound.push(rv);
    else badReal++;
  }
  return judge(c, roots.length, sound, badReal);
}

function judge(