papers/lp-220-p3q-corona/sections/05-dex-rollup-settlement.tex

\section{Application: DEX Rollup Settlement to Z-Chain}
\label{sec:dex-rollup}

The DEX matching path (Lux Lightspeed DEX~\cite{luxlightspeeddex}) fills
orders at hundreds of millions per second per GPU on the D-Chain, far
above any single chain's finality rate. To anchor that throughput
trustlessly, per-market fill batches roll up to the Z-Chain and are
verified there through the P3Q family at slot \texttt{0x012205}. This
section places Corona (kind $0x02$) in that settlement pipeline; the
measured verify rates belong to the sibling kinds, and Corona is the
optional Module-LWE parameter-diversity leg.

\subsection{Two verification rungs}

DEX rollup settlement uses a two-rung ladder, both callable at the same
P3Q slot:

\begin{enumerate}[leftmargin=2em,nosep]
  \item \textbf{Attestation rung (venue-trust).} The sequencer signs each
    per-market batch with a P3Q kind~$0x01$ (Pulsar / FIPS-204 ML-DSA-65)
    threshold signature. The Z-Chain contract calls
    \texttt{P3Q.verify(0x01, \ldots)} to confirm the batch was produced
    by the venue's threshold quorum. This rung trusts the venue's signer
    set but is cheap: the ML-DSA-65 verify path is measured at
    $\sim$\num{4714} verifies per second.
  \item \textbf{Validity rung (trustless).} For trust-minimized
    settlement the sequencer additionally produces a STARK/FRI validity
    proof of correct matching, verified by the \texttt{starkfri} verifier
    (LP-221~\cite{lp221}) --- a cSHAKE256 / Goldilocks PQ Plonky3-fork
    verifier. This rung proves the fills are correct without trusting the
    signer set. The current verifier is measured at $\sim$\num{986}
    proofs per second against a \textbf{toy AIR}; this figure is the
    operative number and is explicitly not a production-circuit
    measurement.
\end{enumerate}

The attestation rung is fast and venue-trusting; the validity rung is
slower and trustless. A venue chooses the rung (or runs both) per its
trust requirements.

\subsection{Where Corona fits}

Corona (kind $0x02$) is the \emph{Module-LWE cross-family insurance leg}
for the attestation rung, not a separate settlement mechanism. A
value-bearing DEX rollup that wants independence from the Module-LWE
assumption underlying ML-DSA-65 signs each batch with \emph{both} a
Pulsar (kind $0x01$) and a Corona (kind $0x02$) threshold signature and
requires both \texttt{P3Q.verify} calls to return \texttt{true}, exactly
as in Section~\ref{sec:corona-kind}'s use case. A Module-LWE break that
compromises the Pulsar attestation does not compromise the Corona
attestation; the rollup's settlement remains cryptographically anchored.

The cost discipline of Section~\ref{sec:corona-kind} applies unchanged:
Corona's \SI{5000000}{gas} makes the second leg appropriate for
value-bearing markets (custody, treasury, regulated-securities venues)
and prohibitive for high-volume markets, which settle on the kind~$0x01$
attestation rung alone (optionally backed by the starkfri validity rung).
As noted throughout this paper, Corona's GPU dispatch is projected and
its verifier core is not yet wired; the DEX settlement path that needs a
second lattice family today uses the measured kind~$0x01$ rung, with
Corona reserved at its dispatch entry until its threshold library lands.

\subsection{Bundled settlement: $K \times V \times \text{markets}$}

Per-fill, per-venue verification does not scale: at the
attestation-rung's $\sim$\num{4714} verifies per second, a chain that
verified one signature per fill would cap settlement far below the
matcher's fill rate. The settlement model therefore bundles. A single
Z-Chain settlement object aggregates $K$ signer attestations across $V$
venues across many markets into one verification event:

\begin{itemize}[leftmargin=2em,nosep]
  \item \textbf{$K$ signers.} The threshold quorum per venue contributes
    $K$ partial signatures aggregated into one threshold signature that
    verifies in a single \texttt{P3Q.verify} call.
  \item \textbf{$V$ venues.} Independent venues' batches are aggregated
    into one settlement object rather than verified one venue at a time.
  \item \textbf{Many markets.} Each venue's per-market arenas (Lux
    Lightspeed DEX) contribute their batch roots to the bundle, so a
    single verification covers many books.
\end{itemize}

Because one verification amortizes over $K \times V \times
\text{markets}$ fills, the effective settled-fill rate at fleet scale is
\textbf{projected} to exceed $10^9$ fills per second of finality ---
this is a fleet-aggregation projection, not a single-verifier
measurement. The per-verifier measured rates ($\sim$\num{4714}/s
attestation, $\sim$\num{986}/s validity on a toy AIR) are the operative
numbers; the $>$$10^9$ figure is what those rates compose to once the
bundle factor $K \times V \times \text{markets}$ is applied across a
multi-node Z-Chain settlement fleet. No single P3Q verifier reaches that
rate.

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