Protocol Invariants - x0 Protocol

Core Invariants

These invariants are enforced on-chain and must hold at all times. Violation of any invariant halts the transaction.

1. Spend Limit Invariant (x0-guard)

\sum_{i \in W} a_i + a_{\text{new}} \leq L_{\text{daily}}

Where:

$W$ is the set of spending entries within the rolling 24-hour window
$a_i$ is the amount of each spending entry
$a_{\text{new}}$ is the proposed transfer amount
$L_{\text{daily}}$ is the agent’s configured daily limit

Enforcement: Checked in the transfer hook before every transfer. Stale entries (older than 24 hours) are pruned before the check.

2. Per-Transaction Limit Invariant

a_{\text{new}} \leq L_{\text{tx}}

Where

L_{\text{tx}}

is the maximum single transaction amount (maxSingleTransaction). Enforcement: Checked in the guard before every transfer. Error: SingleTransactionLimitExceeded (0x1141).

3. Reserve Invariant (x0-wrapper)

R_{\text{USDC}} \geq S_{\text{x0\text{-}USD}}

Where:

$R_{\text{USDC}}$ is the USDC balance held in the reserve account
$S_{\text{x0\text{-}USD}}$ is the total outstanding x0-USD supply

Enforcement: Checked after every deposit and redemption. Error: ReserveInvariantViolated (0x1611). Corollary: The redemption fee ensures the reserve is always slightly overcollateralized:

R_{\text{USDC}} \geq S_{\text{x0\text{-}USD}} \cdot \left(1 + \frac{f}{10000}\right)

Where

f

is the redemption fee in basis points.

4. Delegation Invariant (x0-guard)

\text{agent\_signer} \neq \text{owner}

The agent and owner must be different keys. Error: SelfDelegationNotAllowed (0x111A).

5. Bound Account Invariant (x0-guard)

\text{source\_account.owner} = \text{policy.owner}

The source token account must be owned by the policy owner. Error: TokenAccountOwnerMismatch (0x1119).

6. Escrow State Machine Invariant

The escrow state can only transition through valid paths:

Created → Funded → Delivered → Released
                 → Disputed  → Released | Refunded
       → Cancelled (only from Created)
Funded → Refunded (via timeout)
Delivered → Released (via auto-release timeout)

Any attempt to transition to an invalid state results in InvalidEscrowState (0x1109).

7. Confidential Amount Bound

0 \leq a \leq 2^{48} - 1

All confidential transfer amounts must be representable in 48 bits. Error: AmountExceedsConfidentialMax (0x150F) or AmountTooLarge (0x1710).

8. Proof Freshness Invariant

t_{\text{now}} - t_{\text{verified}} \leq 300 \text{ seconds}

ZK proof contexts expire after 5 minutes. Stale proofs cannot be used for transfers. Error: ProofExpired (0x1704).

9. Fee Bounds Invariant (x0-wrapper)

10 \leq f_{\text{bps}} \leq 500

The wrapper redemption fee must stay within governance-defined bounds (0.1% to 5.0%). Errors: FeeRateTooLow (0x1625) or FeeRateTooHigh (0x1624).

10. Timelock Invariant (x0-wrapper)

t_{\text{execute}} \geq t_{\text{scheduled}} + 172{,}800

Admin actions cannot be executed before the 48-hour timelock expires. Error: TimelockNotExpired (0x1643). Exception: emergency pause bypasses the timelock.

Derived Properties

These properties follow from the core invariants:

Property	Follows From	Implication
Maximum loss from compromised agent	Invariant 1	At most $L_{\text{daily}}$ can be spent in any 24-hour window
x0-USD is always redeemable	Invariant 3	Every x0-USD in circulation is backed by at least 1 USDC
Agent cannot self-authorize	Invariant 4	Agent always operates under owner’s delegated authority
Proofs are non-replayable	Invariant 8	A proof context can only be used once within its 5-minute window
Governance changes are observable	Invariant 10	Community has 48 hours to react to any admin action

Automated Checks

The on-chain programs enforce these invariants automatically. The SDK also provides client-side helper functions for pre-flight validation:

import { PolicyManager, WrapperClient } from '@x0-protocol/sdk';

// Check spend limit before submitting
const policy = await client.getMyPolicy();
if (client.policy.wouldExceedSpendLimit(policy, transferAmount)) {
  console.log('Transfer would exceed daily limit');
}

// Check reserve health
const wrapper = new WrapperClient(connection);
const stats = await wrapper.fetchStats();
const healthy = wrapper.isReserveHealthy(
  stats.reserveUsdcBalance,
  stats.outstandingWrapperSupply
);

Security

​Core Invariants

​1. Spend Limit Invariant (x0-guard)

​2. Per-Transaction Limit Invariant

​3. Reserve Invariant (x0-wrapper)

​4. Delegation Invariant (x0-guard)

​5. Bound Account Invariant (x0-guard)

​6. Escrow State Machine Invariant

​7. Confidential Amount Bound

​8. Proof Freshness Invariant

​9. Fee Bounds Invariant (x0-wrapper)

​10. Timelock Invariant (x0-wrapper)

​Derived Properties

​Automated Checks