papers/chain-first-architecture/sections/02-formal-model.tex

\section{Formal Model}

\label{sec:model}
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\subsection{System State}

\begin{definition}[Chain State]
The chain state at block $h$ is a function
$\mathcal{C}_h : \text{Address} \times \text{Token} \rightarrow
\mathbb{N}$ mapping each (address, token) pair to a balance.
The genesis state $\mathcal{C}_0$ is defined by the genesis
configuration.  For $h > 0$:
\[
  \mathcal{C}_h = \mathcal{T}_h(\mathcal{C}_{h-1})
\]
where $\mathcal{T}_h$ is the deterministic state transition function
defined by the transactions in block $h$.
\end{definition}

\begin{definition}[Cache State]
The cache state $\mathcal{D}_h$ is maintained by the indexer.  For
each chain event $e$ emitted by block $h$, the indexer applies a
deterministic update $\delta(e)$ to the cache:
\[
  \mathcal{D}_h = \delta(e_1) \circ \delta(e_2) \circ \cdots \circ
  \delta(e_k)(\mathcal{D}_{h-1})
\]
where $e_1, \ldots, e_k$ are the events in block $h$.
\end{definition}

\begin{definition}[Consistency]
The system is \emph{consistent at block $h$} if and only if:
\[
  \forall \, (a, t) : \mathcal{D}_h(a, t) = \mathcal{C}_h(a, t)
\]
That is, the cache reflects the chain state for every address and
token.
\end{definition}

\subsection{Settlement Pipeline}

The pipeline from API request to on-chain settlement:

\begin{enumerate}[nosep]
  \item \textbf{API receives order.}  The order is validated
        (authentication, authorization, compliance checks) and
        recorded in the \texttt{pending\_orders} table.
  \item \textbf{Matching engine matches order.}  The matched trade
        is recorded in the \texttt{trades} table and the
        \texttt{pending\_settlements} table.
  \item \textbf{Settlement cron fires (30s interval).}  For each
        pending settlement:
        \begin{enumerate}[nosep]
          \item Construct the on-chain transaction (mint target token,
                burn source token).
          \item Initiate MPC signing (2-of-3 threshold).
          \item Broadcast the signed transaction.
        \end{enumerate}
  \item \textbf{Chain confirms transaction.}  The transaction is
        included in a block.
  \item \textbf{Indexer processes block.}  The indexer reads the
        block's events and updates the cache.  The
        \texttt{pending\_settlements} entry is marked as confirmed.
  \item \textbf{Cache serves reads.}  The API layer reads balances,
        positions, and transaction history from the cache.
\end{enumerate}

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