numpy>=1.24.0      # Numerical operations
pandas>=2.0.0      # Data manipulation
scipy>=1.10.0      # Statistical functions
matplotlib>=3.7.0  # Visualization
seaborn>=0.12.0    # Statistical visualization

hashlib            # SHA256, RIPEMD160
ecdsa>=0.18.0      # Elliptic curve operations
base58>=2.1.0      # Bitcoin address encoding

def helix_gate_ternary(a, b, c):
    """
    Helix Gate ternary output.
    Input: Three integer values
    Output: Ternary value {-1, 0, +1}
    """
    total = a + b + c
    return (total % 3) - 1
 
def apply_helix_chain(values, gate_size=3):
    """
    Apply Helix Gate across sequence.
    Input: List of values
    Output: List of ternary outputs
    """
    result = []
    for i in range(len(values) - gate_size + 1):
        a, b, c = values[i], values[i+1], values[i+2]
        result.append(helix_gate_ternary(a, b, c))
    return result

def extract_patoshi_blocks(start=0, end=50000):
    """
    Extract Patoshi-pattern blocks from blockchain.
    Returns: List of block objects with pubkey data
    """
    blocks = []
    for height in range(start, end):
        block = get_block(height)
        if is_patoshi_pattern(block.nonce):
            blocks.append({
                'height': height,
                'pubkey': block.coinbase_pubkey,
                'timestamp': block.timestamp
            })
    return blocks

from scipy import stats
 
# Chi-squared test for block distribution
observed = [8, 10, 10, 10, 5, 4, 0, 3, 2, 1]
expected = [5.3] * 10
 
chi2, p_value = stats.chisquare(observed, expected)
print(f"Chi-squared: {chi2:.4f}")
print(f"P-value: {p_value:.6f}")
# Output: Chi-squared: 26.0566, P-value: 0.002000

// 3D terrain generation from matrix values
const geometry = useMemo(() => {
  const geo = new THREE.PlaneGeometry(10, 10, 127, 127);
  const positions = geo.attributes.position;
 
  for (let i = 0; i < positions.count; i++) {
    const ix = i % 128;
    const iy = Math.floor(i / 128);
    const value = matrix[127 - iy]?.[ix] ?? 0;
    const normalized = (value - stats.min) / (stats.max - stats.min);
    positions.setZ(i, (normalized - 0.5) * heightScale);
  }
 
  return geo;
}, [matrix, stats]);

bitcoin-cli getblock <hash> 2 | jq '.tx[0].vout[0].scriptPubKey'

# Load from exported JSON
with open('anna-matrix.json', 'r') as f:
    data = json.load(f)
matrix = data['matrix']  # 128x128 signed byte array

sha256sum anna-matrix.json
# Expected: [published checksum]

# Clone repository
git clone [repository-url]
 
# Install dependencies
pip install -r requirements.txt
 
# Run verification suite
python scripts/verification/run_all_tests.py