#!/usr/bin/env python3
from __future__ import annotations

import json
import math
import sys
from pathlib import Path


def independent_bound(row: dict) -> float:
    eigenvalues = row["prior_eigenvalues"]
    d = row["d"]
    horizon = row["T"]
    q = 24.0 * math.log(horizon) / d
    c1 = math.sqrt(1.0 + max(q, math.sqrt(q)))
    c2 = 2.0 * c1 * math.sqrt(math.log(1.0 + row["radius"] ** 2 * max(eigenvalues) * horizon / (d * row["sigma"] ** 2)))
    return (
        d * row["sigma"] * math.sqrt(horizon) * c2
        + 3.0 * math.sqrt(2.0) * row["radius"] * math.sqrt(d) * sum(math.sqrt(value) for value in eigenvalues) * c1
        + math.sqrt(2.0 * row["radius"] ** 2 * sum(eigenvalues))
    )


def main() -> None:
    evidence = json.loads(Path(sys.argv[1]).read_text())
    rows = evidence["rows"]
    relative_errors = [abs(independent_bound(row) - row["theorem_1_bound"]) / row["theorem_1_bound"] for row in rows]
    checks = {
        "all_covariance_eigenvalues_positive": all(min(row["prior_eigenvalues"]) > 0 for row in rows),
        "all_actions_use_positive_radius": all(row["radius"] > 0 for row in rows),
        "formula_reconstruction_matches": max(relative_errors) < 1e-12,
        "confidence_intervals_finite": all(math.isfinite(row["regret_ci95_low"]) and math.isfinite(row["regret_ci95_high"]) for row in rows),
        "legacy_column_has_exact_sqrt_T_multiplier": all(abs(row["legacy_multiplicative_burnin_scale"] / row["corollary_burnin_scale"] - math.sqrt(row["T"])) < 1e-12 for row in rows),
    }
    output = {"passed": all(checks.values()), "checks": checks, "max_formula_relative_error": max(relative_errors)}
    print(json.dumps(output, sort_keys=True))
    raise SystemExit(0 if output["passed"] else 1)


if __name__ == "__main__":
    main()