papers/zoo-poai-consensus/sections/01-introduction.tex

\section{Introduction}

Proof of AI asks a harder question than whether a provider signed a result: did the
committed AI computation actually run, under the job and execution policy the network
accepted? Useful work cannot secure a monetary system merely because it is expensive.
The work must be demand-backed, objectively bound, cheaper to verify than to perform,
available for challenge, finalized exactly once, and connected to a consequence authority
that fails closed.

The Lux architecture assigns those responsibilities to one canonical path. A requester
submits a job to the A-Chain; a miner executes it under a versioned deterministic kernel
profile and emits a canonical transcript; validators check the required execution,
availability, graph, metering, and anti-replay obligations; A-Chain consensus alone
finalizes the job, consumes its nullifier, and authorizes \textsc{AI}. The finalized
transition is then settled through P3Q on Z-Chain and finalized by Lux Quasar. Other chains
may receive a receipt and payout, but cannot replace the A-Chain as the mining authority.

\subsection{Challenges}

\begin{enumerate}
  \item \textbf{Execution}: distinguish genuine computation from a signed guess or copied output.
  \item \textbf{Determinism}: give heterogeneous miners and CPU validators one exact statement to check.
  \item \textbf{Cost asymmetry}: keep verification materially cheaper than the original workload.
  \item \textbf{Completeness}: bind the full accepted graph, inputs, outputs, artifacts, availability, and meter.
  \item \textbf{Consensus}: ensure one authority admits, finalizes, nullifies, and authorizes each reward.
\end{enumerate}

\subsection{Contributions}

This paper contributes:

\begin{enumerate}
  \item an exact-integer, software-only Freivalds construction for challenged matrix
  products, with $1/p$ soundness per vector and CPU-verifiable $O(n^2)$ checks against the
  miner's $O(n^3)$ dense multiplication;
  \item a versioned deterministic kernel profile fixing arithmetic, layouts, accumulator
  widths, overflow, reductions, fixed-point scales, rounding, tie-breaking, and encodings;
  \item a canonical transcript binding the A-Chain job and policy, model/runtime/input
  commitments, ordered graph operations, outputs, metering, provider, destination, and
  nonce into the root challenged and later settled;
  \item anti-replay, anti-substitution, graph-coverage, and receipt-soundness obligations
  that prevent a correct local check from being mistaken for proof of the whole job;
  \item a single-authority omnichain topology: A-Chain PoAI consensus, Z-Chain P3Q
  settlement, Lux Quasar post-quantum finality, and receipt-only exactly-once payout to
  Zoo or any other destination; and
  \item an explicit implementation ledger separating proven primitives and reference
  fixtures from the production model, availability, metering, A-Chain, and P3Q integration
  still required before public mining activation.
\end{enumerate}

The construction proves objective execution under committed artifacts. It does not prove
that an output is true, aligned, or valuable. Demand, pricing, and governed quality remain
market questions; consensus decides only whether the committed eligible work occurred and
whether its one reward may issue.