"""F5-conf-03: counterexample to proposition A and baseline check for B.

Run from workspace root: ~/wp29/venv/bin/python out/analysis.py
Reads only data/; writes out/results.json and out/counterexample.csv.
"""
import json
from pathlib import Path

import numpy as np
import pandas as pd
from scipy import stats

ROOT = Path(__file__).resolve().parent.parent
DATA, OUT = ROOT / "data", ROOT / "out"

props = pd.read_csv(DATA / "propositions.csv")
design = pd.read_csv(DATA / "design.csv")
data_issues = []
assert set(props["id"]) == {"A", "B"}, "propositions.csv must contain A and B"
par = dict(zip(design["parameter"], design["value"]))
seed, n = int(par["seed"]), int(par["n"])
assert n > 0

def summ(a):
    return float(np.mean(a)), float(np.std(a, ddof=1))

def ks_vs_fitted_normal(s):
    m, sd = summ(s)
    return float(stats.kstest(s, "norm", args=(m, sd)).statistic)

rng = np.random.default_rng(seed)
# Counterexample to A: X ~ N(0,1); S ~ Rademacher(+-1 w.p. 1/2) independent of X; Y = S*X.
# Y ~ N(0,1) by symmetry of N(0,1); X+Y = (1+S)X equals 0 w.p. 1/2 and 2X w.p. 1/2.
x = rng.standard_normal(n)
s = rng.choice(np.array([-1.0, 1.0]), size=n)
y = s * x
total = x + y

pd.DataFrame({"x": x, "y": y}).to_csv(OUT / "counterexample.csv", index=False)

mx, sx = summ(x); my, sy = summ(y); ms, ss = summ(total)
ks_sum = ks_vs_fitted_normal(total)
# Additional illustrative diagnostics (marginal KS vs fitted normal; atom at zero)
ks_x, ks_y = ks_vs_fitted_normal(x), ks_vs_fitted_normal(y)
frac_sum_zero = float(np.mean(total == 0.0))

# Baseline for B (same evaluation rule): independent X, Y ~ N(0,1), separate stream
rng_b = np.random.default_rng([seed, 1])
xb, yb = rng_b.standard_normal(n), rng_b.standard_normal(n)
ks_b = ks_vs_fitted_normal(xb + yb)

results = {
    "task_id": "F5-conf-03",
    "statement_true": False,
    "counterexample_provided": True,
    "counterexample_values": {
        "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), Cov(X,Y)=0, and X+Y = (1+S)X is 0 with probability 1/2 "
                         "and 2X ~ N(0,4) with probability 1/2 (a non-degenerate mixture with an atom at 0, not normal)."),
        "n": int(n), "seed": seed,
        "mean_x": mx, "sd_x": sx, "mean_y": my, "sd_y": sy,
        "mean_sum": ms, "sd_sum": ss,
        "ks_sum_vs_normal": ks_sum,
    },
    "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,
    "diagnostic_ks_x_vs_normal": ks_x,
    "diagnostic_ks_y_vs_normal": ks_y,
    "diagnostic_frac_sum_exactly_zero": frac_sum_zero,
    "diagnostic_ks_critical_value_alpha_0.05": float(1.358 / np.sqrt(n)),
    "baseline_independent_ks_sum_vs_normal": ks_b,
    "baseline_independent_seed_spec": "numpy default_rng([seed, 1])",
}
with open(OUT / "results.json", "w") as f:
    json.dump(results, f, indent=2)
print(json.dumps(results, indent=2))