Terminology

Term	Definition
PGOLD	PGOLD is a tokenized representation of gold, designed to provide digital ownership of physical gold assets. It serves as the core collateral within the system.
PGUSD	PGUSD is a stablecoin derived from PGOLD, pegged to the U.S. dollar. It is implemented as an ERC‑20 token and used for stable transactions and liquidity.
LPGOLD	LPGOLD is a leveraged tokenized gold asset split from PGOLD. It is implemented as an ERC‑1155 token and represents exposure to leveraged gold positions.
$LTV_t$	Loan‑to‑Value ratio at time t measures the proportion of borrowed value relative to the collateral. It is a key risk metric in lending and collateral management.
$NAV_t$	Net Asset Value at time t represents the value of LPGOLD holdings at that specific moment. It reflects the dynamic worth of leveraged gold positions.
LP	LP refers to liquidity providers who supply assets to the trading pool. They earn fees and play a crucial role in maintaining market liquidity.
AMM	AMM is a custom automated market maker pool built for trading. It contains USDC and PGUSD, enabling decentralized swaps and price discovery.
$N_G$	$N_G$ denotes the initial amount of PGOLD collateral deposited by a user. It represents the starting gold‑backed position in the system.
$N_S$	$N_S$ represents the initial quantity of PGUSD obtained by the user. It reflects the stablecoin allocation derived from PGOLD collateral.
$N_L$	$N_L$ is the initial amount of LPGOLD allocated to the user. It captures the leveraged exposure to gold at the beginning of the position.
$P_t$	$P_t$ is the price of PGOLD at time t. It serves as the market reference for valuation, collateral calculations, and trading decisions.