"""F5-conf-03: counterexample to 'sum of normals is normal' (prop. A) and check of B.
Run from workspace root: ~/wp29/venv/bin/python out/analysis.py
Construction: X ~ N(0,1), S ~ Rademacher(+-1 w.p. 1/2) independent of X, Y = S*X.
Y ~ N(0,1) (X symmetric, S independent); X+Y = (1+S)X equals 0 w.p. 1/2 and 2X otherwise
-> has an atom at 0 yet Var = 2 > 0, so it is neither non-degenerate normal nor constant.
"""
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 = os.path.join(ROOT, "data"); O = 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"])
data_issues = []
assert set(props["id"]) == {"A", "B"}, "unexpected proposition ids"

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)

def ks_fit(v):
    return float(stats.kstest(v, "norm", args=(v.mean(), v.std(ddof=1))).statistic)

cv = {
    "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) but X+Y = (1+S)X is 0 with prob. 1/2 and 2X otherwise (atom at 0, Var 2).",
    "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(z.mean()), "sd_sum": float(z.std(ddof=1)),
    "ks_sum_vs_normal": ks_fit(z),
}
# supplementary diagnostics (marginals vs fitted normal, atom share, independence-based baseline for B)
supp = {
    "ks_x_vs_normal": ks_fit(x), "ks_y_vs_normal": ks_fit(y),
    "share_sum_exactly_zero": float(np.mean(z == 0.0)),
    "ks_critical_value_5pct_approx": float(1.358 / np.sqrt(n)),
    "corr_xy": float(np.corrcoef(x, y)[0, 1]),
}
rng_b = np.random.default_rng(seed + 1)  # separate stream for the B illustration only
xb, yb = rng_b.standard_normal(n), rng_b.standard_normal(n)
baseline = {"baseline_b_indep_ks_sum_vs_normal": ks_fit(xb + yb),
            "baseline_b_indep_sd_sum": float((xb + yb).std(ddof=1)),
            "baseline_b_seed": seed + 1}

res = {
    "task_id": "F5-conf-03",
    "statement_true": False,           # by proof in out/argument.md
    "counterexample_provided": True,
    "counterexample_values": cv,
    "statement_b_true": True,          # by proof (characteristic functions) in out/argument.md
    "feasibility": "complete",
    "feasibility_reason": None,
    "data_issues": data_issues,
    "n_input_rows": {"propositions.csv": int(len(props)), "design.csv": int(len(design))},
    "n_analysed": int(n),
    "random_seed": seed,
    "supplementary_diagnostics": supp,
    **baseline,
}
with open(os.path.join(O, "results.json"), "w") as f:
    json.dump(res, f, indent=2)
print(json.dumps(res, indent=2))