1[2 {"id": "C1", "text": "Proposition A is false: Y = S*X with S an independent Rademacher sign gives N(0,1) marginals while X+Y ~ 0.5*delta_0 + 0.5*N(0,4) is neither normal nor constant.", "results_keys": ["statement_true", "counterexample_provided", "counterexample_values"], "status": "supported", "caveat": "Truth value rests on the proof in out/argument.md; the simulation is illustrative."},3 {"id": "C2", "text": "Proposition B is true: characteristic functions of independent normals multiply to a normal characteristic function.", "results_keys": ["statement_b_true"], "status": "supported", "caveat": "Proof sketch; standard result."},4 {"id": "C3", "text": "In the simulated sample (seed 20261029, n=100000) the marginals are consistent with N(0,1) while the sum departs strongly from normality (KS 0.2508 vs ~0.004 noise; ~50% exact zeros).", "results_keys": ["counterexample_values", "counterexample_diagnostics", "n_analysed", "random_seed"], "status": "supported", "caveat": "Numerical illustration only; KS with estimated parameters is approximately calibrated."},5 {"id": "C4", "text": "The baseline independent-normal sum is consistent with normality (KS 0.0020), in line with B.", "results_keys": ["baseline_b_ks_sum_vs_normal", "baseline_b_sd_sum"], "status": "supported", "caveat": "Consistency check, not a proof."}6]7