Verifying Results

Crypta will immediately reveal to the public each hash after it is used.

Anyone can independently:

1) Verify that the Hash is Part of the Original Committed Chain:

$$SHA512(H_{n}) = H_{n+1}$$

2) Verify the Randomness Hash:

$$SHA512(H_n + Salt) = pmHASH_n$$

You can use any independent third party SHA-512 hash generator for step 1 and 2 or run the Python code below.

If verifying only the chain hash, leave salt_hash = "".

import hashlib

# === Step 1: Input the revealed hash and optional salt ===
chain_hash = "e1f4c3b2a8d1234567890abcdeffedcba9876543210ffeeddccbbaa9988776655"
salt_hash  = ""  # Leave empty to verify the chain only

# === Step 2: Concatenate and hash ===
combined_text = chain_hash + salt_hash
pmHASH = hashlib.sha512(combined_text.encode()).hexdigest()

print("pmHASH:", pmHASH)

• If salt_hash is left empty, the result is the next hash in the chain (Hₙ₊₁).

• If salt_hash is filled in, the result is the randomness hash (pmHASH) used to generate price movements.

3) Verify the Price Movements from the pmHASH:

Use the python code below to derive the price movements generated from any pmHASH:

import math

# === User Inputs ===
pmHASH = "af939b318736bb7dc7eb6014770097572eeb28d82a329cdefa70b6e79ba4c46ddadbf9a1a34d2c25be1771ad6c16be127a51b4ef43c9f03db3e44fd4ed836743"
standard_deviation = 5.0  # You can change this if needed

# === Price Movement Derivation ===
def derive_price_movements_from_pmhash(pm_hash: str, sigma: float = 5.0):
    movements = []
    for i in range(8):
        start = i * 13
        end = start + 13
        hex_block = pm_hash[start:end]
        u_int = int(hex_block, 16)
        u_prime = u_int / 2**52

        if i % 2 == 1:
            u1 = movements[-1]["u_prime"]
            u2 = u_prime
            if u1 == 0:
                u1 = 1e-10
            z0 = math.sqrt(-2.0 * math.log(u1)) * math.cos(2 * math.pi * u2)
            z1 = math.sqrt(-2.0 * math.log(u1)) * math.sin(2 * math.pi * u2)
            movements[-1]["m"] = z0 * sigma
            movements.append({"u_prime": u2, "m": z1 * sigma})
        else:
            movements.append({"u_prime": u_prime})

    return [round(m["m"], 6) for m in movements]

# === Run the Derivation ===
price_movements = derive_price_movements_from_pmhash(pmHASH, standard_deviation)
print("Price Movements:", price_movements)

Summary

• Hash Chain Integrity: Confirm that SHA512(Hₙ) == Hₙ₊₁ to verify the hash is part of the committed chain.

• Randomness Integrity: Confirm that SHA512(Hₙ + salt) equals the published pmHASH.

• Movement Verification: Use the pmHASH to generate 8 reproducible price movements via the documented Box-Muller transformation.