Math Reference

WAD                  = 10^18
USD_VALUE_DECIMALS   = 9
BASIS_POINTS         = 10_000
SECONDS_PER_YEAR     = 31_536_000
BALANCE_TO_BORROW    = 1.1 × WAD
CLOSE_FACTOR_BPS     = 5_000
MIN_INITIAL_SHARES   = 1_000

u_bps = floor(borrows × 10_000 / (cash + borrows))

if u ≤ u_opt:
  rate_bps = base + floor(slope1 × u / u_opt)
else:
  rate_bps = base + slope1 + floor(slope2 × (u − u_opt) / (10_000 − u_opt))

interest = ceil(total_borrow × rate_bps × elapsed / (10_000 × SECONDS_PER_YEAR))
fee      = floor(interest × reserve_factor_bps / 10_000)
total_borrow' = total_borrow + interest
fees'         = fees + fee
index'        = index × (total_borrow' / total_borrow)   // WAD

lender_assets = cash + borrows − fees

supply_shares = floor(assets × total_shares / lender_assets)   // 1:1 if empty
redeem_assets = floor(shares × lender_assets / total_shares)

new_shares  = ceil(assets × total_borrow_shares / total_borrow_assets)  // 1:1 if empty
user_debt   = ceil(user_shares × total_borrow_assets / total_borrow_shares)
repay_share = floor(paid × total_borrow_shares / total_borrow_assets)

value = token_amount × price × 10^(exp − decimals + 9)
HF    = collateral_usd / debt_usd
ok    ⇔ HF > 1.1

repay    ≤ 50% of that debt
seize_usd = repay_usd × (10_000 + bonus_bps) / 10_000
seize_tok = value_to_token_amount(seize_usd, …)