"""F5-conf-03: regenerate out/results.json and out/counterexample.csv from data/ only.
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

os.makedirs("out", exist_ok=True)
props = pd.read_csv("data/propositions.csv")
design = pd.read_csv("data/design.csv")
d = dict(zip(design["parameter"], design["value"]))
seed = int(d["seed"]); n = int(d["n"])

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

# Verdicts rest on the mathematical argument in out/argument.md, not on simulation.
statement_A_true = False   # counterexample: Y = S*X, S Rademacher independent of X
statement_B_true = True    # independent normals: characteristic functions multiply

rng = np.random.default_rng(seed)
x = rng.standard_normal(n)
s = rng.choice(np.array([-1.0, 1.0]), size=n)   # independent Rademacher sign
y = s * x
z = x + y
pd.DataFrame({"x": x, "y": y}).to_csv("out/counterexample.csv", index=False)

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

cv = {
    "construction": "X ~ N(0,1); S independent of X with P(S=1)=P(S=-1)=1/2; Y = S*X. "
                    "Then Y ~ N(0,1) by symmetry of N(0,1), but X+Y = (1+S)X equals 0 with prob. 1/2 "
                    "and 2X (N(0,4)) with prob. 1/2: a non-degenerate law with an atom at 0, hence not normal.",
    "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_vs_fitted(z),
}

# Supplementary diagnostics (illustration only)
diag = {
    "frac_sum_exactly_zero": float(np.mean(z == 0.0)),
    "ks_x_vs_std_normal": float(stats.kstest(x, "norm").statistic),
    "ks_y_vs_std_normal": float(stats.kstest(y, "norm").statistic),
    "ks_x_vs_fitted_normal": ks_vs_fitted(x),
    "ks_y_vs_fitted_normal": ks_vs_fitted(y),
    "corr_xy": float(np.corrcoef(x, y)[0, 1]),
}
# Population sup distance between law of X+Y (0.5*delta_0 + 0.5*N(0,4)) and N(0,2)
# (normal with the same mean 0 and variance 2), on a fine grid incl. both sides of the jump at 0.
grid = np.linspace(-10, 10, 200001)
F_mix = 0.5 * (grid >= 0) + 0.5 * stats.norm.cdf(grid, scale=2.0)
F_mix_left = 0.5 * (grid > 0) + 0.5 * stats.norm.cdf(grid, scale=2.0)
G = stats.norm.cdf(grid, scale=np.sqrt(2.0))
diag["population_ks_sum_vs_N02"] = float(max(np.abs(F_mix - G).max(), np.abs(F_mix_left - G).max()))
diag["ks_95pct_critical_value_approx"] = float(1.358 / np.sqrt(n))

# Baseline for B (independent case), same seed stream continued, same KS rule
xb = rng.standard_normal(n); yb = rng.standard_normal(n)
baseline = {"baseline_b_ks_sum_vs_normal": ks_vs_fitted(xb + yb),
            "baseline_b_sd_sum": float((xb + yb).std(ddof=1))}

results = {
    "task_id": "F5-conf-03",
    "statement_true": statement_A_true,
    "counterexample_provided": True,
    "counterexample_values": cv,
    "statement_b_true": statement_B_true,
    "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,
    "counterexample_diagnostics": diag,
    **baseline,
}
with open("out/results.json", "w") as f:
    json.dump(results, f, indent=2)
print(json.dumps({k: results[k] for k in ("statement_true", "statement_b_true")}),
      "KS(sum)=%.4f" % cv["ks_sum_vs_normal"], "baseline KS(B)=%.4f" % baseline["baseline_b_ks_sum_vs_normal"])