"""F5-conf-03: counterexample to proposition A and numerical check of B.
Run from workspace root: ~/wp29/venv/bin/python out/analysis.py
Reads only data/; writes out/results.json, out/counterexample.csv, out/exclusions.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"])

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

rng = np.random.default_rng(seed)
# Counterexample construction (drawn first from the seeded generator):
# X ~ N(0,1), S ~ Rademacher independent of X, Y = S*X.
x = rng.standard_normal(n)
s = rng.choice(np.array([-1.0, 1.0]), size=n)
y = s * x
z = x + y

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

def ks_std(v):  # vs N(0,1) exactly (theoretical marginal)
    return float(stats.kstest(v, "norm").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 equals 0 w.p. 1/2 and 2X otherwise "
                    "(mixture of a point mass at 0 and N(0,4)), which is 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_fit(z),
    # supplementary diagnostics
    "ks_x_vs_std_normal": ks_std(x), "ks_y_vs_std_normal": ks_std(y),
    "frac_sum_exactly_zero": float(np.mean(z == 0.0)),
    "ks_critical_5pct_approx": float(1.358 / np.sqrt(n)),
}
pd.DataFrame({"x": x, "y": y}).to_csv(os.path.join(O, "counterexample.csv"), index=False)

# Baseline (proposition B): independent X, Y ~ N(0,1), drawn after the counterexample
xb = rng.standard_normal(n); yb = rng.standard_normal(n); zb = xb + yb
baseline = {"construction": "X, Y iid N(0,1), drawn from the same generator after the counterexample draws",
            "mean_sum": float(zb.mean()), "sd_sum": float(zb.std(ddof=1)),
            "ks_sum_vs_normal": ks_fit(zb)}

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": data_issues,
    "n_input_rows": {"propositions.csv": int(len(props)), "design.csv": int(len(design))},
    "n_analysed": int(n),
    "random_seed": seed,
    "baseline_independent_sum": baseline,
}
with open(os.path.join(O, "results.json"), "w") as f:
    json.dump(res, f, indent=2)
pd.DataFrame([{"step": 0, "rule": "none (no filtering; simulated sample of size n)", "n_before": n,
               "n_after": n, "n_removed": 0, "rationale": "design-specified simulation, nothing excluded"}]
             ).to_csv(os.path.join(O, "exclusions.csv"), index=False)
print(json.dumps({k: res[k] for k in ["statement_true", "statement_b_true", "n_analysed"]}),
      "KS sum:", cv["ks_sum_vs_normal"], "baseline KS:", baseline["ks_sum_vs_normal"])