"""F5-conf-03: counterexample to proposition A; regenerates out/results.json and out/counterexample.csv."""
import json, os
import numpy as np, pandas as pd
from scipy import stats

ROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
D, O = os.path.join(ROOT, "data"), os.path.join(ROOT, "out")
props = pd.read_csv(os.path.join(D, "propositions.csv"))
design = pd.read_csv(os.path.join(D, "design.csv"))
par = dict(zip(design["parameter"], design["value"]))
seed, n = int(par["seed"]), int(par["n"])

issues = []
if set(props["id"]) != {"A", "B"}:
    issues.append({"issue": "unexpected proposition ids", "handling": "assessed as listed"})

# Construction: X ~ N(0,1), S ~ Rademacher independent of X, Y = S*X.
rng = np.random.default_rng(seed)
x = rng.standard_normal(n)
s = rng.choice(np.array([-1.0, 1.0]), size=n)
y = s * x
z = x + y
pd.DataFrame({"x": x, "y": y}).to_csv(os.path.join(O, "counterexample.csv"), index=False)

mz, sz = z.mean(), z.std(ddof=1)
ks = stats.kstest(z, "norm", args=(mz, sz)).statistic
ks_x = stats.kstest(x, "norm", args=(x.mean(), x.std(ddof=1)))
ks_y = stats.kstest(y, "norm", args=(y.mean(), y.std(ddof=1)))

res = {
    "task_id": "F5-conf-03",
    "statement_true": False,
    "counterexample_provided": True,
    "counterexample_values": {
        "construction": "X ~ N(0,1); S ~ Rademacher (P(S=1)=P(S=-1)=1/2) independent of X; Y = S*X. "
                        "Then Y ~ N(0,1) by symmetry, but X+Y = (1+S)X equals 0 with probability 1/2 "
                        "and 2X otherwise (Var = 2), so X+Y has an atom at 0 and is neither normal nor constant.",
        "n": int(n), "seed": seed,
        "mean_x": float(x.mean()), "sd_x": float(x.std(ddof=1)),
        "mean_y": float(y.mean()), "sd_y": float(y.std(ddof=1)),
        "mean_sum": float(mz), "sd_sum": float(sz),
        "ks_sum_vs_normal": float(ks),
        "supplementary": {
            "share_sum_exactly_zero": float(np.mean(z == 0)),
            "ks_x_vs_fitted_normal": float(ks_x.statistic), "ks_x_pvalue": float(ks_x.pvalue),
            "ks_y_vs_fitted_normal": float(ks_y.statistic), "ks_y_pvalue": float(ks_y.pvalue),
            "corr_xy": float(np.corrcoef(x, y)[0, 1]),
            "excess_kurtosis_sum": float(stats.kurtosis(z)),
        },
    },
    "statement_b_true": True,
    "feasibility": "complete",
    "feasibility_reason": None,
    "data_issues": issues,
    "n_input_rows": {"propositions.csv": int(len(props)), "design.csv": int(len(design))},
    "n_analysed": int(n),
    "random_seed": seed,
}
with open(os.path.join(O, "results.json"), "w") as f:
    json.dump(res, f, indent=2)
print(json.dumps(res, indent=2))