"""Law-9 audit of THE THREE-HALVES ECHO — independent Python reproduction.

Different language, different code, same definitions (read from the C++
instrument and from THE SIBLING SIGN's lineage):
  fine_r(k):  Pearson r of x_j = 2*A[2^k + j] - (2^k + j) vs
              y_j = 2*A[2^(k-1) + j] - (2^(k-1) + j), j in [0, 2^(k-1)).
  env_r(k):   64-bin mean-|2A[n]-n| profiles of block [2^k, 3*2^(k-1))
              vs block [2^(k-1), 2^k), each z-normalized (population sd),
              dot/64.
Targets: published fine/env k=22 (old lamp) and NEW fine/env k=27.
Needs A up to 3*2^26 - 1 = 201,326,591; clock gate at 2^27 included.
"""
import sys, time
from array import array
import numpy as np

K = 27
N = 3 * (1 << (K - 1))  # 201,326,592 — covers fine/env at k=27
A = array('I', bytes(4 * (N + 1)))
A[1] = A[2] = 1

t0 = time.time()
BENCH = 10_000_000
a = A  # local alias
for n in range(3, BENCH):
    p = a[n - 1]
    a[n] = a[p] + a[n - p]
rate = (BENCH - 3) / (time.time() - t0)
eta = (N + 1 - BENCH) / rate
print(f"[meter] {rate/1e6:.2f}M steps/s; remaining ~{eta/60:.1f} min for {N:,}", flush=True)

for n in range(BENCH, N + 1):
    p = a[n - 1]
    a[n] = a[p] + a[n - p]
print(f"[meter] recurrence done in {(time.time()-t0)/60:.1f} min total", flush=True)

# gates: range (sampled full-strength via vector check) + exact clock
V = np.frombuffer(A, dtype=np.uint32)
idx = np.arange(1, N + 1, dtype=np.int64)
if not ((V[1:N+1] >= 1).all() and (V[1:N+1] <= idx).all()):
    sys.exit("range breach")
for k in range(1, K + 1):
    if A[1 << k] != 1 << (k - 1):
        sys.exit(f"clock breach k={k}")
print("[audit] range + clock gates PASSED", flush=True)

def fine_r(k):
    half = 1 << (k - 1)
    x0, y0 = 1 << k, half
    x = 2.0 * V[x0:x0+half] - np.arange(x0, x0 + half, dtype=np.float64)
    y = 2.0 * V[y0:y0+half] - np.arange(y0, y0 + half, dtype=np.float64)
    x -= x.mean(); y -= y.mean()
    return float((x @ y) / np.sqrt((x @ x) * (y @ y)))

def env_profile(lo, hi, bins=64):
    E = np.abs(2.0 * V[lo:hi] - np.arange(lo, hi, dtype=np.float64))
    p = E.reshape(bins, -1).mean(axis=1)
    return (p - p.mean()) / p.std()

def env_r(k):
    lo = 1 << k
    x = env_profile(lo, lo + (1 << (k - 1)))
    y = env_profile(1 << (k - 1), 1 << k)
    return float((x @ y) / 64)

for k, fw, ew in ((22, 0.29829476, 0.29812658), (27, 0.30136301, 0.30119130)):
    f, e = fine_r(k), env_r(k)
    tag = "OLD-LAMP" if k == 22 else "NEW-RUNG"
    ok = abs(f - fw) < 5e-9 and abs(e - ew) < 5e-9
    print(f"[{tag}] k={k} fine={f:+.8f} (want {fw:+.8f})  env={e:+.8f} (want {ew:+.8f})  "
          + ("MATCH all 8 decimals" if ok else "MISMATCH"), flush=True)
    if not ok:
        sys.exit(9)
print("[audit] independent reproduction PASSED — old lamp k=22 and new rung k=27, both grains")