{
  "verdict": "accept",
  "issues": [
    {
      "id": "R1",
      "severity": "minor",
      "location": "out/argument.md, out/report.md (theoretical KS ~0.25)",
      "issue": "The sum's 'theoretical KS distance of about 0.25 (half of the jump of 1/2 at 0)' is stated without derivation. It is in fact a lower bound: the fitted N(0,2) CDF equals 0.5 at 0, while the population CDF jumps from 0.25 to 0.75 there. The exact supremum is not shown.",
      "suggested_fix": "Add the one-line argument that sup|F - Phi| >= 0.25 because of the atom at 0, and call 0.25 a lower bound."
    }
  ],
  "summary": "I re-ran analysis.py in a scratch copy and got results.json and counterexample.csv back byte for byte (n=100000, seed 20261029, 50.047% of sums exactly 0). All required keys are present and correctly computed: ddof=1 SDs, and a KS distance against a normal fitted with the sample mean and SD. The code reads only data/ and follows the design seed and n. The proof for B (characteristic functions) and the random-sign counterexample for A (normal marginals by symmetry; the sum has an atom of 1/2 at 0 and variance 2, so it is neither a non-degenerate nor a degenerate normal) are both correct. The report keeps the illustration separate from the proof and states its limits. Numbers in the report and claims match results.json, including the ~120x and ~58x ratios, the 0.0043 critical value and the SE statements. The B baseline is present. The only issue is minor wording."
}