papers/zoo-desci-platform/sections/07-formal-verification-of-research-claims.tex

\section{Formal Verification of Research Claims}

\label{sec:verification}
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\subsection{The Trust Problem in Mathematical Results}

Published mathematical results are trusted because peer reviewers checked them. But peer review is fallible: errors in published proofs are discovered regularly, sometimes decades later. For results that underpin critical infrastructure (cryptographic protocols, safety-critical systems), informal trust is insufficient.

\subsection{Lean 4 Proof Chain}

\Zoo{} integrates Lean~4 \cite{demoura2021lean4} formal verification into the research publication pipeline:

\begin{enumerate}
    \item The researcher states a theorem in Lean~4.
    \item The proof is developed interactively, with each step machine-checked.
    \item The completed proof is compiled to a proof certificate.
    \item The certificate hash is anchored on \IChain{} alongside the Research Capsule.
    \item Any verifier can download the proof and re-check it independently.
\end{enumerate}

\subsection{Proof-Linked Publications}

A Research Capsule containing a formal proof links the following chain:

\begin{equation}
\textit{theorem} \xrightarrow{\text{Lean 4}} \textit{proof} \xrightarrow{\text{BLAKE3}} \textit{hash} \xrightarrow{\text{IChain}} \textit{anchor}
\end{equation}

This creates an immutable, machine-verified record that the theorem was proved (not merely claimed) at the time of publication.

\subsection{Verified Cryptographic Claims}

For \Zoo{}'s own cryptographic infrastructure, formal verification provides a trust foundation:

\begin{itemize}
    \item \CKKS{} rescaling correctness (\texttt{Crypto/FHE/CKKS.lean}) \cite{zoo-fhe}
    \item \textsc{TFHE} noise budget tracking (\texttt{Crypto/FHE/TFHE.lean})
    \item Threshold signature security (\texttt{Crypto/Threshold/FROST.lean})
    \item GPU scaling bounds (\texttt{GPU/FHEScaling.lean})
\end{itemize}

These proofs are anchored on \IChain{} and linked from the corresponding technical papers, allowing anyone to verify that the security claims are not merely argued but proved.

\subsection{Incentivizing Formalization}

Formalizing existing results is valuable but tedious. \Zoo{} incentivizes it:

\begin{itemize}
    \item \textbf{Formalization Bounties.} \DAO{} treasury funds bounties for formalizing high-impact results.
    \item \textbf{Reputation Rewards.} Formalization efforts accrue reputation on the researcher's \DID{}.
    \item \textbf{Citation Credit.} A formalized proof cites the original result, generating a usage receipt and compensation for the original authors.
\end{itemize}

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