papers/zoo-poai-consensus/zoo-poai-consensus.tex

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% Title and authors
\title{\textbf{Proof of AI: A Consensus Mechanism for Verifiable Compute Contribution}\\
\large CPU-verifiable useful work on Lux A-Chain with post-quantum omnichain settlement}
\author{
Antje Worring, Zoo Labs Foundation Research\thanks{[email protected]}\\
\textit{Hanzo AI \quad Lux Network \quad Zoo Labs Foundation}\\
\texttt{[email protected]}
}

\date{August 2026}

\begin{document}

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\begin{abstract}
We introduce \textbf{Proof of AI} (\PoAI{}), the useful-work consensus of the Lux
A-Chain. A demand-backed job is admitted before mining; a provider performs genuine AI
execution and commits a proof artifact produced alongside it. The public proof-bearing
profile requires software only---no trusted execution environment and no GPU attestor---so
an ordinary CPU can validate challenged work without repeating the original GPU workload.
The recomputable ``hash everyone can check'' becomes a canonical execution transcript
whose activation commitments cannot be forged without answering for the genuine matrix
multiplications. We give one primitive realizing four
execution-level proofs over a workload tag---Proof-of-Embedding, Proof-of-Inference,
Proof-of-Training, and a privacy-preserving Proof-of-Contribution---by committing the
computation trace and spot-checking its matmuls with Freivalds' algorithm over the
int8 path's exact integer accumulator, which yields a bit-exact check with soundness
error $1/p \approx 2^{-61}$ per vector ($2^{-122}$ at $k{=}2$) and \emph{zero} false
rejections. We bind every proof to its task with a domain-separated,
beacon-fresh, measured-model commitment, and prove anti-substitution and anti-replay
for it. We position the scheme as Bitcoin's shared, software-only difficulty---the
Hamiltonian Market Maker \emph{prices} heterogeneous compute while the execution proof
\emph{verifies} it, two orthogonal dials---and give a single profile gate mapping tiers
(zkML, $M$-of-$N$ confidential compute, optimistic-Freivalds, redundancy) to required
proof strength, designed so that once the gate is engaged ``no valid compute proof''
means ``no mint.'' We motivate the construction with a concrete reference-engine attack
in which a one-bit guess could satisfy a receipt path, because a signature proves
authorship and a plurality proves agreement, but neither proves computation. Optional
TEE attestation, multi-party scoring, and redundancy may supplement the public profile;
the execution proof is what binds reward to genuine work, and Lux Quasar supplies the
post-quantum consensus/finality layer.

\textbf{Status, stated up front.} This paper proves an arithmetic primitive and reports
tested reference surfaces: an exact-integer Freivalds verifier, transcript and graph
fixtures, matching encodings in Rust and Go, and fail-closed EVM prototypes. These results
support the construction but do not constitute a live A-Chain mining path. A complete Zen
model does not yet emit the production transcript on its normal serving path, and the
A-Chain node does not yet admit the job, verify finalized evidence, enforce data
availability and metering, consume the nullifier, and authorize issuance through this
system. P3Q settlement is likewise audit- and activation-gated. Section~\ref{sec:status-summary}
gives the ledger before the construction. The honest summary is: \emph{the primitive and
reference fixtures are built and tested; production emission, availability, A-Chain
consensus wiring, metering, and P3Q settlement remain integration work}.

\textbf{The \Zoo{} reading.} \Zoo{} Labs Foundation is an application and research layer
for decentralized AI and decentralized science. It may submit jobs, fund work, and consume
final receipts, but it is not a second Proof-of-AI chain. Section~\ref{sec:l3-settlement}
shows the single-authority topology: A-Chain alone admits and finalizes useful work,
Z-Chain settles finalized receipt transitions through P3Q, Lux Quasar supplies
post-quantum finality, and Zoo applications consume the resulting receipts.

\textbf{Keywords}: consensus, proof of useful work, AI compute verification, Freivalds'
algorithm, optimistic verification, decentralized science, omnichain settlement,
post-quantum cryptography, verifiable machine learning
\end{abstract}

\input{sections/01-introduction}
\input{sections/00-status-summary}
\input{sections/02-background}
\input{sections/03-poai}
\input{sections/04-compute-verification}
\input{sections/05-quality-scoring}
\input{sections/06-security-analysis}
\input{sections/07-experimental-evaluation}
% ── Execution-level proofs: the software-only, Bitcoin-style provable-AI scheme ──
\input{sections/11-guess-to-mint-attack}
\input{sections/15-binding-scheme}
\input{sections/16-four-proofs}
\input{sections/17-freivalds-hash}
\input{sections/18-shared-difficulty}
\input{sections/19-tier-matrix}
\input{sections/20-ownership}
% ── The formal core: the Receipt Soundness theorem + the 16 invariants ──
\input{sections/25-receipt-soundness}
% ── Full modern-LLM coverage: fp-vs-quantized tiering, the zen zoo, build status ──
\input{sections/21-modern-llm-coverage}
\input{sections/22-architecture-families}
% ── Zoo L3: settlement of PoAI-verified work + DeSci/DeAI reproducibility substrate ──
\input{sections/24-zoo-l3-settlement}
\input{sections/23-implementation-status}
% ── Original material ──
\input{sections/08-related-work}
\input{sections/09-future-work}
\input{sections/10-conclusion}
\input{sections/12-attestation-format}
\input{sections/13-quality-scoring-functions}
\input{sections/14-slashing-conditions}
\input{sections/99-acknowledgments}

\end{document}