Share-Based Accounting

Why Shares?

Traditional balance tracking has problems at scale - updating every user's balance on every interest accrual is O(n) complexity and causes rounding errors to accumulate differently per user.

Share-based accounting solves this by updating a single global index (O(1) complexity), and deriving user balances on-demand by multiplying their shares by the current index. All users share the same index, eliminating drift.

Core Data Model

Position Structure

Each user position stores shares, not native balances:

• deposit_scaled - supply shares
• debt_scaled - debt shares

Native balances are derived:

• deposit_native = deposit_scaled × lending_index
• debt_native = debt_scaled × borrow_index

Pool Indices

Each pool maintains two indices that grow over time:

• lending_index - cumulative supply growth (starts at 1.0)
• borrow_index - cumulative debt growth (starts at 1.0)
• last_updated - timestamp of last sync

Balance Calculation

Supply balance: deposit_native = deposit_scaled × lending_index

Debt balance: debt_native = debt_scaled × borrow_index

Share Operations

Minting Shares (Deposit/Borrow)

When a user deposits or borrows, shares are minted based on the current index:

shares = native_amount / index

Example Deposit: User deposits 100 tokens at lending_index = 1.05 → shares_minted = 100 / 1.05 = 95.24 shares

Burning Shares (Withdraw/Repay)

When a user withdraws or repays, shares are burned:

Example Withdraw: User withdraws after index grows to 1.10 → shares_burned = 95.24 shares → native_received = 95.24 × 1.10 = 104.76 tokens (earned 4.76 tokens interest)

Interest Accrual Example

Initial State (t=0):

• lending_index = 1.0, borrow_index = 1.0
• Alice deposits 1000 tokens → 1000 shares
• Bob borrows 500 tokens → 500 debt shares

After 1 Year:

• Pool utilization = 50%
• Borrow rate = 5.125%, Lending rate = 2.306%
• New indices: borrow_index = 1.0526, lending_index = 1.0231

Balances:

• Alice: 1000 shares × 1.0231 = 1023.1 tokens (+2.31% APY)
• Bob: 500 shares × 1.0526 = 526.3 tokens debt (+5.26% APY)
• Interest gap: 26.3 - 23.1 = 3.2 tokens (protocol revenue)

RAY Precision

All index calculations use RAY precision (1e27) to maintain accuracy. This matches Aave's implementation and provides enough precision for tokens with up to 9 decimals plus 18 digits of buffer.

Index Synchronization

Before any operation, the pool's indices must be synchronized to the current time:

This ensures all operations use up-to-date indices for accurate share calculations.

Key Invariants

1. Indices never decrease - they only grow (monotonic)
2. Shares only change on user actions - deposit/withdraw/borrow/repay/liquidate
3. Protocol revenue = debt interest - supply interest
4. All calculations use RAY precision (1e27)