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zeekay e16498a49a poai: add the formal core — Receipt Soundness theorem + the 16 invariants
New section "The Formal Core: Receipt Soundness" (sections/25). States exactly what
Proof-of-AI proves — the five objective lifecycle properties (identity, execution,
provenance, accounting, settlement) — and refuses the semantic claims (truth,
alignment, usefulness), citing the verification-horizon result for why no fixed
semantic verifier stays sound.

- The universal AIReceipt object + its canonical reportData/receiptId commitment.
- The orthogonal contract surface (AIJob/AIReceipt/AIProof/AISettle/AIModel/AIEngine/
  AIData/AIStore/AICompute) and the one-way dataflow.
- The proof-tier ladder + the finalization gate: ProofType in AllowedProofTypes(jobType)
  and ProofLevel >= MinProofLevel(jobType); fail-closed.
- The nine provable job classes, each with its objective verifier statement.
- The 16 invariants (I1-I16) with by-construction / tested / staged status, mapped to
  the real contracts and the 474-test suite.
- Theorem (Receipt Soundness) + corollaries (Inference, Training-Lineage, Accounting,
  Governance Safety) with proof sketches.
- The honest boundary + the one-line truth.

Compiles clean, 56 pages; verificationhorizon added to the bibliography.
2026-06-26 00:31:59 -07:00

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\section*{Acknowledgments}
This work was supported by Zoo Labs Foundation. We thank Intel for SGX documentation and AMD for SEV-SNP technical support.
\bibliographystyle{plain}
\begin{thebibliography}{99}
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S. King, ``Primecoin: Cryptocurrency with Prime Number Proof-of-Work,'' 2013.
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Gridcoin, ``Rewarding BOINC Contributions,'' Whitepaper, 2014.
\bibitem{mcmahan2017communication}
B. McMahan et al., ``Communication-Efficient Learning of Deep Networks from Decentralized Data,'' \textit{AISTATS}, 2017.
\bibitem{boneh2001bls}
D. Boneh et al., ``Short Signatures from the Weil Pairing,'' \textit{ASIACRYPT}, 2001.
\bibitem{costan2016sgx}
V. Costan and S. Devadas, ``Intel SGX Explained,'' \textit{Cryptology ePrint}, 2016.
\bibitem{buchman2018tendermint}
E. Buchman et al., ``The latest gossip on BFT consensus,'' \textit{arXiv:1807.04938}, 2018.
\bibitem{freivalds1979}
R. Freivalds, ``Fast probabilistic algorithms,'' in \textit{Mathematical Foundations of Computer Science (MFCS)}, LNCS 74, pp.\ 57--69, 1979.
\bibitem{opml2024}
KD. Conway, C. So, X. Yu, and K. Wong, ``opML: Optimistic Machine Learning on Blockchain,'' \textit{arXiv:2401.17555}, 2024.
\bibitem{gensynverde}
J. Harrison et al. (Gensyn), ``Verde: Verification via Refereed Delegation for Machine Learning Programs,'' \textit{arXiv:2502.19405}, 2025.
\bibitem{arbitrum}
H. Kalodner et al., ``Arbitrum: Scalable, private smart contracts,'' \textit{USENIX Security}, 2018.
\bibitem{hyperbolicposp}
Hyperbolic Labs, ``Proof of Sampling (PoSP): A Verification Protocol for Decentralized AI Inference,'' Technical Report, 2024.
\bibitem{gkr2008}
S. Goldwasser, Y.~T. Kalai, and G.~N. Rothblum, ``Delegating Computation: Interactive Proofs for Muggles,'' \textit{STOC}, 2008.
\bibitem{lund1992sumcheck}
C. Lund, L. Fortnow, H. Karloff, and N. Nisan, ``Algebraic Methods for Interactive Proof Systems,'' \textit{Journal of the ACM}, 39(4):859--868, 1992.
\bibitem{ezkl2024}
J. Chen et al., ``ezkl: A System for Zero-Knowledge Machine Learning,'' \url{https://github.com/zkonduit/ezkl}, 2024.
\bibitem{nvidiacc}
NVIDIA Corporation, ``NVIDIA Confidential Computing on Hopper H100 / Blackwell: Architecture and Attestation,'' Technical Whitepaper, 2023--2024.
\bibitem{inteltdx}
Intel Corporation, ``Intel Trust Domain Extensions (Intel TDX) Whitepaper,'' 2023.
\bibitem{amdsevsnp}
AMD, ``AMD SEV-SNP: Strengthening VM Isolation with Integrity Protection and More,'' Technical Whitepaper, 2020.
\bibitem{repbla}
J. Demmel and H.~D. Nguyen, ``Parallel Reproducible Summation,'' \textit{IEEE Transactions on Computers}, 64(7):2060--2070, 2015.
\bibitem{ieee754}
IEEE, ``IEEE Standard for Floating-Point Arithmetic,'' \textit{IEEE Std 754-2019}, 2019.
\bibitem{gu2023mamba}
A. Gu and T. Dao, ``Mamba: Linear-Time Sequence Modeling with Selective State Spaces,'' \textit{arXiv:2312.00752}, 2023.
\bibitem{yang2024deltanet}
S. Yang, B. Wang, Y. Zhang, Y. Shen, and Y. Kim, ``Parallelizing Linear Transformers with the Delta Rule over Sequence Length,'' \textit{NeurIPS}, 2024.
\bibitem{zhou2024transfusion}
C. Zhou et al., ``Transfusion: Predict the Next Token and Diffuse Images with One Multi-Modal Model,'' \textit{arXiv:2408.11039}, 2024.
\bibitem{shazeer2017moe}
N. Shazeer et al., ``Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer,'' \textit{ICLR}, 2017.
\bibitem{poisoundness}
Zoo Labs Foundation, ``Proof-of-Inference: Soundness, the Determinism Liveness Precondition, the Floating-Point No-Go, and the Routing/Chaining Extension Obligations,'' companion soundness report, \texttt{zooai/proofs:proof-of-inference-soundness.tex}, 2026. Contains the per-result status table ``What is proven on code versus on paper.''
\bibitem{poiemission}
Zoo Labs Foundation, Hanzo AI, and Lux Network, ``Proof-of-Inference: End-to-End Emission and On-Chain Enforcement---the activation-trace commitment that makes \textit{no real compute, no mint} a theorem,'' companion emission report, \texttt{zooai/proofs:proof-of-inference-emission.tex}, 2026. Tabulates the cross-language implementation (Rust prover, Go verifier, Solidity witness/precompile) and the adversarial red-team battery.
\bibitem{verificationhorizon}
``The Verification Horizon: No Silver Bullet for Coding Agent Rewards,'' 2026. Establishes that semantic verification of agent output is a proxy for human intent that degrades as generator capability grows---motivating \PoAI{}'s split between provable execution and the un-provable semantic remainder.
\end{thebibliography}
\appendix