papers/hanzo-checkout/sections/02-system-model-and-definitions.tex

\section{System Model and Definitions}


\subsection{Payment Transaction Model}

\begin{definition}[Payment Transaction]
A payment transaction $T$ is a tuple $(m, c, a, p, \sigma)$ where:
\begin{itemize}
    \item $m \in \mathcal{M}$: merchant identifier
    \item $c \in \mathcal{C}$: customer identifier
    \item $a \in \mathbb{R}^+$: transaction amount
    \item $p \in \mathcal{P}$: payment method token
    \item $\sigma$: cryptographic signature binding the transaction
\end{itemize}
\end{definition}

\begin{definition}[Checkout State]
The checkout state $S$ is an element of the state space:
\[
S \in \{INIT, CUSTOMER\_IDENTIFIED, PAYMENT\_SELECTED, AUTHORIZED, CAPTURED, COMPLETED, FAILED\}
\]
\end{definition}

\subsection{State Transition Function}

The checkout process is governed by a deterministic state transition function:

\begin{equation}
\delta: S \times \Sigma \rightarrow S \times \Gamma
\end{equation}

where $\Sigma$ is the set of input events and $\Gamma$ is the set of output actions.

\begin{definition}[One-Click Eligibility]
A customer $c$ is one-click eligible for merchant $m$ if:
\begin{equation}
eligible(c, m) \iff \exists p \in tokens(c) : valid(p) \land authorized(p, m)
\end{equation}
\end{definition}