"""Replication entry point for F5-conf-03.
Run from workspace root:  ~/wp29/venv/bin/python out/analysis.py
Reads only data/, writes out/results.json and out/counterexample.csv deterministically.

Counterexample to A: X ~ N(0,1); W independent of X with P(W=1)=P(W=-1)=1/2; 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,
so it has an atom of mass 1/2 at 0 and is not a constant -> not normal (not even degenerate).
"""
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__)))
DATA = os.path.join(ROOT, "data")
OUT = os.path.join(ROOT, "out")

props = pd.read_csv(os.path.join(DATA, "propositions.csv"))
design = pd.read_csv(os.path.join(DATA, "design.csv"))
data_issues = []
assert set(props["id"]) == {"A", "B"}, "unexpected proposition ids"
d = dict(zip(design["parameter"], design["value"]))
seed, n = int(d["seed"]), int(d["n"])

# Verdicts: from the mathematical argument in out/argument.md (not from the simulation).
statement_true = False      # A is false (counterexample below)
statement_b_true = True     # B is true (characteristic-function / convolution proof)

# ---- Counterexample sample (order of draws fixed: x first, then w) ----
rng = np.random.default_rng(seed)
x = rng.standard_normal(n)
w = rng.choice(np.array([-1.0, 1.0]), size=n)
y = w * x
s = x + y

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

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

cv = {
    "construction": ("X ~ N(0,1); W independent of X with P(W=1)=P(W=-1)=1/2; Y = W*X. "
                     "Then Y ~ N(0,1), and X+Y = (1+W)X is 0 with probability 1/2 and 2X otherwise "
                     "(atom of mass 1/2 at 0, non-constant), hence not normal."),
    "n": int(len(x)),
    "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(s.mean()), "sd_sum": float(s.std(ddof=1)),
    "ks_sum_vs_normal": ks_vs_fitted_normal(s),
}

# ---- Supplementary diagnostics (same KS rule) ----
# Baseline for B: independent normal partner Z drawn AFTER the counterexample draws from the same rng
z = rng.standard_normal(n)
supp = {
    "ks_x_vs_normal": ks_vs_fitted_normal(x),
    "ks_y_vs_normal": ks_vs_fitted_normal(y),
    "share_sum_exactly_zero": float(np.mean(s == 0.0)),
    "baseline_ks_independent_sum_vs_normal": ks_vs_fitted_normal(x + z),
    "corr_x_y": float(np.corrcoef(x, y)[0, 1]),
    "note": ("baseline_* uses Z ~ N(0,1) independent of X (proposition B setting), drawn after x and w "
             "from the same generator; KS statistics use parameters estimated from the sample."),
}

results = {
    "task_id": "F5-conf-03",
    "statement_true": statement_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(len(x)),
    "random_seed": seed,
    "supplementary": supp,
}
with open(os.path.join(OUT, "results.json"), "w") as f:
    json.dump(results, f, indent=2)
print(json.dumps(results, indent=2))