#!/usr/bin/env python3
"""CFL bound verification sweep for Burgers step correspondence."""
import random, math, json, hashlib
from datetime import datetime, timezone

Q16 = 65536
random.seed(42)

def step(u, N, nu, dx, dt):
    nu_q = int(nu*Q16); dt_q = int(dt*Q16); dx_q = int(dx*Q16)
    new = [0]*N
    for i in range(N):
        ux = ((u[(i+1)%N] - u[(i-1)%N]) // (2*dx_q)) if i>0 and i<N-1 else 0
        uxx = ((u[(i+1)%N] - 2*u[i] + u[(i-1)%N]) // (dx_q*dx_q//Q16)) if i>0 and i<N-1 else 0
        ui = u[i]
        rhs = ((nu_q * uxx) // Q16) - ((ui * ux) // Q16)
        new[i] = u[i] + (dt_q * rhs) // Q16
    return new

def kinetic_energy(u):
    return sum((v*v)//Q16 for v in u) // 2

results = []
for N in [4, 8, 16, 32]:
    for nu in [0.05, 0.1, 0.2]:
        for dt in [0.005, 0.01, 0.02]:
            max_err = 0; max_E0_val = 0
            for _ in range(25):
                u = [0]*N
                for i in range(1, N-1):
                    u[i] = random.randint(-Q16//2, Q16//2)
                E0 = kinetic_energy(u)
                u1 = step(u, N, nu, 1.0, dt)
                E1 = kinetic_energy(u1)
                obs = abs(E1 - E0) / Q16
                max_err = max(max_err, obs)
                max_E0_val = max(max_E0_val, E0/Q16)
            cfl = round(dt * 2.0 * max_E0_val, 6)
            within = max_err < cfl + 0.001
            results.append({
                'N': N, 'nu': nu, 'dt': dt,
                'max_E0': round(max_E0_val, 4),
                'max_step_error': round(max_err, 6),
                'cfl_bound': cfl,
                'within_cfl': within,
            })

receipt = {
    'schema': 'burgers_cfl_sweep_v1',
    'claim_boundary': 'monte_carlo_sweep;cfl_bound_verification',
    'results': results,
    'summary': {
        'total_cases': len(results),
        'all_within_cfl': all(r['within_cfl'] for r in results),
    },
    'computed_at': datetime.now(timezone.utc).isoformat(),
}
canonical = json.dumps(receipt, sort_keys=True, separators=(',', ':'))
receipt['receipt_sha256'] = hashlib.sha256(canonical.encode()).hexdigest()

with open('burgers_cfl_sweep_receipt.json', 'w') as f:
    json.dump(receipt, f, indent=2)

for r in results:
    mark = "✓" if r['within_cfl'] else "✗"
    print(f"N={r['N']:2d} ν={r['nu']:.2f} dt={r['dt']:.3f}  "
          f"E0max={r['max_E0']:6.2f}  err={r['max_step_error']:.6f}  "
          f"CFL={r['cfl_bound']:.6f}  {mark}")
print(f"\nAll within CFL: {receipt['summary']['all_within_cfl']}")
print(f"Receipt: burgers_cfl_sweep_receipt.json")
print(f"SHA256:  {receipt['receipt_sha256']}")