papers/hanzo-ai-chain/sections/07-cross-chain.tex

\section{Post-Quantum Omnichain Settlement}
\label{sec:xchain}

Hanzo's omnichain claim is deliberately asymmetric. Proof-of-AI consensus exists
only on Lux A-Chain. Any supported chain may receive a payout, but no destination
may accept raw work, run a local mining verifier, maintain a competing work-spent
set, or instantiate another AI emission schedule. Z-Chain is the P3Q settlement
rollup for finalized A-Chain transitions, not another PoAI authority.

\subsection{A-Chain work truth, Z-Chain settlement, and Lux finality}

The settlement path is:

\begin{enumerate}[leftmargin=1.4em]
  \item A-Chain admits a useful job and fixes the execution policy, proof policy,
        reward, destination chain, and destination recipient.
  \item A provider commits its output, transcript, and metering after executing
        the job on CPU or GPU.
  \item PoAI consensus resolves the configured proof policy, validates that the
        bound work was actually performed, and consumes the global nullifier.
  \item The final mining receipt is committed under the A-Chain receipt root.
  \item Z-Chain batches the finalized receipt transition and verifies its
        activated Plonky3-derived P3Q STARK/FRI settlement proof. It does not
        reconsider usefulness or accept an unrelated raw-work claim.
  \item Lux Quasar finalizes the corresponding A-Chain and Z-Chain blocks; the
        activated post-quantum validator policy authenticates their roots,
        heights, and validator context.
  \item Warp/Teleport, a native atomic boundary, or an authenticated relay carries
        the Z-settled receipt and inclusion proof to the named destination.
  \item The destination verifies finality, Z settlement, inclusion, chain binding, recipient,
        amount, and local non-consumption, then releases the representation once.
\end{enumerate}

Thus ``mine into chain $D$'' means that the A-Chain job names $D$ before work is
committed. It never means that $D$ can decide whether the work occurred.

\subsection{Receipt object}

A mining receipt binds at least

\begin{equation}
\begin{split}
R=(&\text{job id},\text{work nullifier},\text{miner},\text{model},
\text{input},\text{output},\\
&\text{execution policy},\text{proof policy},\text{proof finality},
\text{measured work},\\
&\text{authorized reward},\text{destination chain},
\text{destination recipient},\text{A-Chain height}).
\end{split}
\end{equation}

The destination acts only on a completed, nonzero, finalized receipt under an
authenticated monotonically advancing Z-settlement root that binds the A-Chain
receipt. A raw miner signature, Freivalds
opening, TEE quote, or output quorum is not an omnichain authorization.

\subsection{Z-Chain P3Q settlement rollup}

P3Q is the intended Plonky3-derived, pairing-free STARK/FRI substrate for
compressing finalized A-Chain receipt transitions on Z-Chain. The statement
proved must include the prior A-Chain receipt root, finalized transition batch,
global-nullifier effects, reward authorizations, and resulting root. Before the
exact PoAI AIR, recursive batching policy, A-to-Z binding, verifier, and node
integration are audited and activated, Z-Chain may record only an independently
authenticated final A-Chain root and must not claim succinct proof authority.

\subsection{Supply conservation}

There is one canonical AI ledger and one proof-earned allowance. A destination
either releases escrowed canonical AI or mints a representation backed by the
canonical settlement rail. It does not reproduce the two-trillion cap, DAO
allocation, halving calculation, or global nullifier. The sum of canonical AI
and unbacked representations must never exceed the canonical supply.

\subsection{C-Chain and external EVMs}

An EVM receipt adapter verifies the Z-settled, PQ-authenticated A-Chain receipt,
Merkle inclusion, destination binding, and exactly-once consumption. Application
contracts may use the receipt to pay a provider, release a model, advance a
workflow, or record provenance. They cannot reinterpret the evidence or award a
different mining amount.

\subsection{F-Chain confidentiality}

F-Chain may supply encrypted execution or confidentiality services to an
A-Chain job. Its ciphertext commitments and output root are bound into the same
PoAI receipt. F-Chain does not become a mining authority, and a confidential
execution profile still requires an explicit proof or attestation policy.

\subsection{M-Chain threshold custody}

M-Chain may custody model keys or authorize confidential-weight release under a
threshold policy. That authorization is an input to the A-Chain job, not proof
that the job ran. Pulsar or Corona may authenticate consensus and custody flows
after their selected protocol and deployment pass review; choosing ML-DSA alone
does not create threshold security.

\subsection{B-Chain and Warp/Teleport transport}

B-Chain, Warp/Teleport, and native atomic interfaces are transport and
settlement mechanisms. Their security obligation is to carry the exact
Quasar-finalized A/Z settlement root and receipt proof without changing the
destination or amount. The same receipt may be relayed by anyone but consumed
only once at its bound destination.

\subsection{Topology summary}

\begin{figure}[h]
\centering
\resizebox{\linewidth}{!}{%
\begin{tikzpicture}[
    node distance=0.8cm and 1.2cm,
    box/.style={rectangle, draw, minimum width=2.2cm, minimum height=0.65cm,
                font=\footnotesize, rounded corners=1pt},
    arrow/.style={->, thick}
]
\node[box] (job) {Useful AI job};
\node[box, right=of job] (a) {A-Chain PoAI};
\node[box, right=of a] (z) {Z-Chain P3Q};
\node[box, right=of z] (lux) {Lux PQ finality};
\node[box, above right=of lux] (hanzo) {Hanzo};
\node[box, right=of lux] (other) {Any destination};
\node[box, below right=of lux] (zoo) {Zoo / Lux / EVM};
\draw[arrow] (job) -- (a);
\draw[arrow] (a) -- node[above,font=\scriptsize]{one receipt} (z);
\draw[arrow] (z) -- node[above,font=\scriptsize]{settled proof} (lux);
\draw[arrow] (lux) -- (hanzo);
\draw[arrow] (lux) -- (other);
\draw[arrow] (lux) -- (zoo);
\end{tikzpicture}
}
\caption{One A-Chain PoAI decision is proved and settled through P3Q on Z-Chain,
then becomes a PQ-authenticated omnichain receipt. Destinations consume it; they
do not validate mining work.}
\end{figure}