"""F5-conf-03: counterexample to 'marginally normal X, Y => X+Y normal'.
Reads data/ only; writes out/results.json and out/counterexample.csv deterministically.
Run from workspace root: ~/wp29/venv/bin/python out/analysis.py
"""
import json, os
import numpy as np
import 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"))
issues = []
assert set(props["id"]) == {"A", "B"}, "unexpected proposition ids"
par = dict(zip(design["parameter"], design["value"]))
seed, n = int(par["seed"]), int(par["n"])
assert float(par["seed"]) == seed and float(par["n"]) == n and n > 0

rng = np.random.default_rng(seed)
# Counterexample construction: X ~ N(0,1), W ~ Rademacher (+/-1 w.p. 1/2) independent of X, Y = W*X.
# Y ~ N(0,1) by symmetry of N(0,1); X+Y = (1+W)X equals 0 w.p. 1/2 and 2X otherwise -> atom at 0, not normal.
x = rng.standard_normal(n)
w = rng.choice(np.array([-1.0, 1.0]), size=n)
y = w * x
s = x + y
pd.DataFrame({"x": x, "y": y}).to_csv(os.path.join(O, "counterexample.csv"), index=False)

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

# Baseline / proposition-B check (same evaluation rule): independent X', Y' ~ N(0,1), drawn after the counterexample.
xb, yb = rng.standard_normal(n), rng.standard_normal(n)
sb = xb + yb

r = lambda v: float(round(v, 10))
cv = {
    "construction": "X ~ N(0,1); W ~ Rademacher (P(W=1)=P(W=-1)=1/2) independent of X; Y = W*X. "
                    "Then Y ~ N(0,1) but X+Y = (1+W)X is 0 with prob. 1/2 and 2X ~ N(0,4) otherwise (atom at 0).",
    "n": int(len(x)), "seed": seed,
    "mean_x": r(x.mean()), "sd_x": r(x.std(ddof=1)),
    "mean_y": r(y.mean()), "sd_y": r(y.std(ddof=1)),
    "mean_sum": r(s.mean()), "sd_sum": r(s.std(ddof=1)),
    "ks_sum_vs_normal": r(ks_vs_fitted_normal(s)),
}
res = {
    "task_id": "F5-conf-03",
    "statement_true": False,
    "counterexample_provided": True,
    "counterexample_values": cv,
    "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(len(x)),
    "random_seed": seed,
    # supplementary diagnostics
    "ks_x_vs_normal": r(ks_vs_fitted_normal(x)),
    "ks_y_vs_normal": r(ks_vs_fitted_normal(y)),
    "frac_sum_exactly_zero": r(np.mean(s == 0.0)),
    "frac_w_equal_1": r(np.mean(w == 1.0)),
    "corr_xy": r(np.corrcoef(x, y)[0, 1]),
    "ks_critical_value_5pct_approx": r(1.358 / np.sqrt(n)),
    "baseline_independent_mean_sum": r(sb.mean()),
    "baseline_independent_sd_sum": r(sb.std(ddof=1)),
    "baseline_independent_ks_sum_vs_normal": r(ks_vs_fitted_normal(sb)),
}
with open(os.path.join(O, "results.json"), "w") as f:
    json.dump(res, f, indent=2)
print(json.dumps(res, indent=2))