# btc16m.py
# Fully folded 16,777,216-vector HDGL Covenant (Logarithmic Expansion)
# Saturates seed vectors conservatively with minimal r_dim + Ω embedding

MAX_SEED_VECTORS = 32         # Number of explicit seed vectors
TARGET_VECTORS = 16_777_216   # 2^24
SAFE_ZERO = "0x0"

# Example r_dim & Ω per seed vector (powers-of-2 scaled for safety)
PARAMS = {
    1: ("0x3000", "0x812"),
    2: ("0x4000", "0x502"),
    3: ("0x5000", "0x310"),
    4: ("0x6000", "0x192"),
    5: ("0x7000", "0x119"),
    6: ("0x8000", "0x73"),
    7: ("0x9000", "0x45"),
    8: ("0xA000", "0x28"),
    # remaining seed vectors repeat last safe saturation
}

def generate_hdgl_16m_covenant(pubkey="<YOUR_PUBLIC_KEY>"):
    script = [f"{pubkey} OP_CHECKSIGVERIFY\n"]

    # --- Step 1: Seed vectors ---
    for idx in range(1, MAX_SEED_VECTORS + 1):
        # Vector block
        v_line = " ".join([SAFE_ZERO]*4) + " OP_HDGL_VEC_ADD OP_EQUALVERIFY"
        script.append(v_line)

        # OP_ADD line
        idx_base = 100 + (idx-1)*4
        add_line = f"{idx_base} {idx_base+1} OP_ADD {idx_base+2} OP_EQUALVERIFY"
        script.append(add_line)

        # OP_WITHINVERIFY line
        within_line = f"{idx_base+3} {idx_base+4} {idx_base+5} OP_WITHINVERIFY"
        script.append(within_line)

        # Embed r_dim & Ω if defined, else repeat last safe value
        param_line = f"{PARAMS.get(idx, ('0xA000','0x28'))[0]} {PARAMS.get(idx, ('0xA000','0x28'))[1]} OP_HDGL_PARAM_ADD OP_EQUALVERIFY"
        script.append(param_line)

        script.append("")  # empty line for readability

    # --- Step 2: Recursive logarithmic folding ---
    current_vectors = MAX_SEED_VECTORS
    fold_idx = MAX_SEED_VECTORS * 4 + 100  # continue indices

    while current_vectors < TARGET_VECTORS:
        v_line = f"OP_VEC_DUP {current_vectors} OP_HDGL_VEC_ADD OP_EQUALVERIFY"
        script.append(v_line)

        add_line = f"{fold_idx} {fold_idx+1} OP_ADD {fold_idx+2} OP_EQUALVERIFY"
        script.append(add_line)

        within_line = f"{fold_idx+3} {fold_idx+4} {fold_idx+5} OP_WITHINVERIFY"
        script.append(within_line)

        script.append("")  # readability
        fold_idx += 6
        current_vectors *= 2

    # --- Step 3: Final covenant verification ---
    script.append("OP_CHECKTEMPLATEVERIFY")

    return "\n".join(script)

if __name__ == "__main__":
    covenant_script = generate_hdgl_16m_covenant()
    print("=== Fully Folded 16,777,216-Vector HDGL Covenant ===")
    print(covenant_script)
