Notation and units

The pages in this section write down what the contracts compute, formula by formula, with the source line each one comes from and a worked example in both raw integers and human units. The narrative pages — interest rates, liquidations, Earn vault — explain why; these explain exactly how much.

Each formula names the contract that computes it, with its mainnet address — for example IsHealthy · 0x9259…F9a1. Contracts deployed once per market (LendingPool, LendingPoolRouter) link to the markets table; a Position is deployed per borrower.

Live values are read from mainnet (chainId 4663), and each names the block it was read at; the parameters page lists them. Mainnet's only debt when these pages were written was about 50 USDG on WETH/USDG, too small to show the rounding, so the worked examples that need a market with debt or a position are illustrative: they use mainnet's parameters and a mainnet price, with round amounts chosen to exercise the formulas. Each says which of its inputs are illustrative.

Scales


WAD	$10^{18}$ . Every ratio, rate and percentage is stored as an integer scaled by it: 100% is `1e18`, 65% is `650000000000000000`, 0.1% is `1e15`
USDG	6 decimals. 1 USDG is `1000000` base units
WETH and every Stock Token (NVDA, SPY, SPCX, TSLA, MSFT, AAPL, QQQ, GOOGL, AMD)	18 decimals
Oracle prices	8 decimals. $250 is `25000000000`
USD values	Health checks convert everything to USD scaled by $10^{18}$
`peUSDG`	The Earn vault's share, 18 decimals

USDG having 6 decimals, not 18, is the single most common integration mistake — a factor of $10^{12}$ .

Time

Y = 365 \times 86{,}400 = 31{,}536{,}000 \text{ seconds}

Every annual rate is converted to per-second with this constant (InterestRateModel · 0x8390…D741). There is no leap-year handling: a year is 365 days exactly.

Symbols

Symbol	Meaning	Where it lives
$S$	Supply assets: what the Earn vault has in a market	`totalSupplyAssets` on the router
$B$	Borrow assets: total debt, including booked interest	`totalBorrowAssets`
$\text{TBS}$	Total borrow shares	`totalBorrowShares`
$R$	Reserves: the protocol's accrued share of interest	`totalReserveAssets`
$A$	The vault's assets: idle USDG plus $\sum S$ over its markets (`totalAssets()` adds pending interest)	`vault.utilizationTotals()`
$U$	Vault-wide utilisation, $\sum B / A$ ; one figure for every market of the vault	`vault.utilization()`
$r$	Borrow rate, an annual rate (APR) in WAD	`calculateBorrowRate(router)`
$R_f$	Reserve factor	interest rate model
$\text{LTV}$ , $\text{LT}$ , $b$	Loan-to-value, liquidation threshold, liquidation bonus	router, IsHealthy
$q$	Collateral in a Position, in base units	`Position.totalCollateral()`
$d$	A borrower's debt in USDG base units	from their shares
$CV$ , $BV$	Collateral value and borrow value, USD × $10^{18}$	IsHealthy

Rounding

Solidity division rounds down. The pages write that as $\lfloor \cdot \rfloor$ , and a round-up (Math.mulDiv(…, Math.Rounding.Ceil)) as $\lceil \cdot \rceil$ . Each rounding moves at most one base unit, but the direction is fixed, and it is worth knowing who each one favours.

Operation	Rounds	Who it favours	Source
Utilisation $U$	down	borrowers (rate slightly lower)	`PaboxoEarnVault · 0xaF5a…c634`
Each slope of the rate curve	down	borrowers	`InterestRateModel · 0x8390…D741`
Interest per accrual	down, once	borrowers, by under one base unit per booking	`InterestRateModel · 0x8390…D741`
Reserve share of interest	down	lenders (they take the remainder)	`InterestRateModel · 0x8390…D741`
Borrow shares minted	down	the borrower (up to one share's worth)	`LendingPoolRouter`
Debt for health checks	down	the borrower	`IsHealthy · 0x9259…F9a1`
Repay: assets pulled for shares	down	the repayer	`LendingPoolRouter`
Close factor: restoring fraction and share cap	up	the liquidator, by at most one share (the position lands on 1.05, never below)	`LendingPoolRouter`
Liquidation: assets paid for shares	up	lenders	`LendingPoolRouter`
Bad debt written off	up	recorded in full	`LendingPoolRouter`
Seize fraction	down	the borrower	`LendingPoolRouter`
Protocol's cut of the seize	down	the liquidator	`LendingPoolRouter`
Borrow fees	down	the borrower	`LendingPoolRouter`
Vault `deposit` / `redeem`	down	the vault	ERC-4626
Vault `mint` / `withdraw`	up	the vault	ERC-4626
Vault `preview*`	as the call it quotes	— previews equal execution	`PaboxoEarnVault · 0xaF5a…c634`
Fee: assets at the high-water mark $A_M$	up	depositors (a gain must be real before it is charged)	`PaboxoEarnVault · 0xaF5a…c634`
Fee: amount $F$ and shares $s_F$	down	depositors	`PaboxoEarnVault · 0xaF5a…c634`

Two asymmetries follow from the table. Repayment rounds in the repayer's favour while liquidation rounds in the lenders'; the repayer's gain is at most one base unit per repayment (under 0.000001 USDG), and it is carried by the remaining borrowers' shares. And a new borrow's shares round down, so the borrower's recorded debt can start up to one share's worth below what they borrowed — again carried by the other borrowers.

APR and APY

Every rate stored or returned on-chain is an APR. Where these pages show an APY it is derived, and they say so — see APR and APY.