Concepts

Core technical concepts behind Zylith.

Concentrated Liquidity (CLMM)

Liquidity providers allocate capital within specific price ranges instead of 0 to infinity.

Constant Product AMM              Concentrated Liquidity
━━━━━━━━━━━━━━━━━━━━━━━           ┌──────────┐
Liquidity: 0 → ∞              ━━━━│██████████│━━━━
                                  └──────────┘
                                  Focused in active range

Tick System

Prices are discretized:

tick = log₁.₀₀₀₁(price)
price = 1.0001^tick

Each tick is ~0.01% price change. LP positions specify tick_lower and tick_upper.

Q128.128 Math

Fixed-point arithmetic for precision:

sqrt_price = sqrt(price) * 2^128

Privacy Model

Commitment Scheme

Two-layer Poseidon hash binding ownership to amount:

inner_hash = Poseidon(secret, nullifier)
commitment = Poseidon(inner_hash, amount)

Component	Purpose	Visibility
secret	Proves ownership	Never revealed
nullifier	Prevents double-spend	Hash revealed on spend
amount	Binds balance	Public input in ZK proof
commitment	On-chain identifier	Public, unlinkable

Verified solvency: Users cannot claim more than deposited because a different amount produces a different commitment that won't exist in the Merkle tree.

Nullifiers

Prevents double-spending:

1. Generate random nullifier at deposit time
2. Store nullifier_hash = Poseidon(nullifier) when spending
3. Contract rejects if nullifier already used

Merkle Trees

BN254 Poseidon Merkle tree (depth 20, ~1M leaves):

         Root
        /    \
       H      H
      / \    / \
     C1  C2 C3  C4  ← Commitments

The ZK proof shows commitment membership without revealing which leaf.

Privacy Pools

Dual Merkle tree architecture for optional compliance:

Deposit Tree                 Association Tree
┌─────────────┐             ┌─────────────┐
│ All deposits│             │ "Clean" only│
└─────────────┘             └─────────────┘

• Deposit Tree: Contains all commitments
• Association Tree: Curated by ASP (relay server), excludes suspicious deposits

Users can prove against either tree—full privacy or compliance proof.

ZK Proofs

Groth16

• Constant-size proofs (~200 bytes)
• Fast verification (~3ms on-chain)
• Requires trusted setup (powers of tau ceremony)
• BN254 curve for Garaga compatibility

Public Inputs

Seven values visible to verifier:

Input	Purpose
root	Merkle tree root
nullifier_hash	Double-spend prevention
recipient	Output commitment
relayer	Fee recipient
fee	Relay fee amount
amount_in	Input amount
min_amount_out	Slippage protection

What the Proof Proves

1. Prover knows secret and nullifier for a commitment
2. That commitment exists in the Merkle tree with given root
3. The amount matches what's encoded in the commitment
4. nullifier_hash = Poseidon(nullifier)

Trust Model

Component	Trust Level	Can	Cannot
Smart Contract	Trustless	-	-
ZK Circuit	Trustless	-	-
Relay Server	Semi-trusted	Censor txs	Steal funds, forge proofs
Browser	User-trusted	Store secrets	Spend without user action