papers/zoo-bridge/sections/03-bridgeable-asset-classes.tex

\section{Bridgeable Asset Classes}

\label{sec:assets}

\subsection{Asset Taxonomy}

\begin{table}[t]
\centering
\begin{tabular}{llll}
\toprule
\textbf{Asset} & \textbf{Lux L0} & \textbf{Zoo L2} & \textbf{Beluga L3} \\
\midrule
Tokens & LUX (native) & ZOO (native) & BLG (native) \\
Model NFTs & --- & ERC-721 & License NFT \\
Data commits & --- & bytes32 hash & Access token \\
Inference credits & --- & ERC-20 (ZINF) & ERC-20 (BINF) \\
\bottomrule
\end{tabular}
\caption{Asset representations across the three-chain ecosystem.}
\label{tab:assets}
\end{table}

\subsection{Token Bridging}

ZOO tokens are bridged between Lux and Zoo via a canonical lock-and-mint mechanism:

\begin{enumerate}
    \item \textbf{Lock}: User deposits ZOO into the bridge contract on Zoo L2
    \item \textbf{Warp}: Bridge emits a Warp message to Lux L0
    \item \textbf{Mint}: Bridge contract on Lux L0 mints wrapped ZOO (wZOO)
    \item \textbf{Reverse}: wZOO burned on Lux $\to$ Warp message $\to$ ZOO unlocked on Zoo
\end{enumerate}

For LUX $\to$ Zoo transfers, the reverse applies: LUX locked on L0, wLUX minted on Zoo.

\subsection{Model NFT Bridging}

Model NFTs require metadata-preserving bridging:

\begin{algorithm}[t]
\caption{Model NFT Bridge Transfer}
\label{alg:nft-bridge}
\begin{algorithmic}[1]
\STATE \textbf{Input}: Model NFT $M$ on Zoo L2, destination Beluga L3
\STATE Lock $M$ in Zoo bridge escrow contract
\STATE Construct metadata payload:
\STATE \quad $p = (\text{tokenId}, \text{modelHash}, \text{arch}, \text{accuracy}, \text{custodyKey})$
\STATE Emit Warp message $W = (\text{Zoo}, \text{Beluga}, p, \sigma)$
\STATE On Beluga L3:
\STATE \quad Verify $\sigma$ against Zoo validator set
\STATE \quad Mint License NFT with metadata from $p$
\STATE \quad License NFT references original model on Zoo via \texttt{modelHash}
\RETURN License NFT on Beluga L3
\end{algorithmic}
\end{algorithm}

The License NFT on Beluga is not a copy of the model; it is a license to invoke inference on the original model hosted on Zoo L2. This preserves the model's custody under Zoo MPC while enabling economic activity on Beluga.

\subsection{Research Data Commitments}

Research data commitments are 32-byte Poseidon2 hashes binding to encrypted data stored on Zoo's data availability layer:

\begin{equation}
C = \text{Poseidon2}(\text{dataHash} \| \text{schemaHash} \| \text{accessPolicy})
\end{equation}

Bridging a data commitment to Beluga creates an access token: an ERC-20 token whose holder can request threshold decryption of the underlying data on Zoo.

\subsection{Inference Credits}

Inference credits (ZINF on Zoo, BINF on Beluga) are exchanged at a floating rate determined by the inference market:

\begin{equation}
\text{rate} = \frac{\text{ZINF\_supply} \cdot \text{avg\_inference\_cost\_zoo}}{\text{BINF\_supply} \cdot \text{avg\_inference\_cost\_beluga}}
\end{equation}

The bridge contract maintains a Uniswap-style constant-product pool for ZINF/BINF conversion.