DUMBHEAD Protocol:Math-Driven, Sybil-Proof Claim System

Transparent · On-Chain · No Admin

🧑‍💻 How the DUMBHEAD Drop Works

Every claim is provable, math-verifiable, and bot-resistant. No admin, no insiders, no chance for whales or scripts. Here’s the protocol behind the world’s first Sybil-proof meme drop.

🌳 Step 1: Merkle Proof of Eligibility

Merkle trees compress a massive eligibility list into a single, unbreakable root hash.
  • Leaf node: H(i, wallet, amount) (Keccak-256)
  • Root hash: Public, fixed at contract launch.
  • Proof: Every claimant submits their leaf and a Merkle proof (just a few hashes, not the full list).
// Example: leaf = keccak256(i || wallet || amount) H(42, "FvA...123", 12000) = "0x0f3e...a6c1"
Security: Impossible to fake your way in. All proofs are public and verifiable.

🧮 Step 2: Anti-Farming via RNS (Residue Number System)

RNS: Instead of storing 100k+ booleans, we use 3 coprime numbers:m₁ = 971,   m₂ = 311,   m₃ = 601
  • For each claim, compute:r₁ = i mod 971
    r₂ = i mod 311
    r₃ = i mod 601
  • If claim_residuesₖ[rₖ] is already set for any k, claim is rejected.
  • If not, all three residues are set to claimed in a single operation.
  • Bit savings: 122 + 39 + 76 = 237 bytes total, not 100,000+ bits!
// Pseudocode: for k in {1,2,3}: if claim_residues_k[i mod m_k] == 1: reject as duplicate else: claim_residues_k[i mod m_k] = 1
Math Proof: Chinese Remainder Theorem: every i < 971×311×601 gets a unique tuple.
Collision probability: 1 in 181 million. (If it happens, you broke the matrix.)

🔗 Step 3: Claim Protocol — End-to-End

  1. Merkle proof: Prove eligibility with your index, wallet, and allocation.
  2. Calculate residues:r₁ = i mod 971
    r₂ = i mod 311
    r₃ = i mod 601
  3. Contract checks: If any residue is set, reject claim.
  4. Set all residues as claimed.
  5. Instant transfer: Tokens sent on-chain.

🧑‍🔬 Math Playground & Range

Claim index: i
Residues:

r₁ = i mod 971
                 r₂ = i mod 311
                  r₃ = i mod 601
                  Uniqueness for 0 ≤ i &lt; 971×311×601 = 181,086,581

For 100,000 users, risk of duplicate: < 0.0006%.

Example: For i = 42, residues are (42, 42, 42). For i = 1,000, residues: (29, 77, 399).
Why is this Secure?
  • Merkle proofs: cryptographically impossible to fake a valid claim.
  • RNS makes duplication/replay practically impossible.
  • No admin—contract is immutable and non-upgradeable after launch.
  • All code & contract state are 100% on-chain and open-source.
Dive deeper into the math and code:
github.com/Takashi-Doyle/merkledrop-rns-contract
Credit: Arthimium Lab, 2025 — built for nerds.