> For the complete documentation index, see [llms.txt](https://docs.moduluszk.io/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.moduluszk.io/references.md). # References ### Papers The three ePrint papers below do different jobs and are kept apart in this documentation. eprint 2024/954. Arithmetisation of computation via polynomial semantics for first-order logic. Murdoch J. Gabbay. Also published in the Journal of Applied Logics 12(6), pp. 1481 to 1548, October 2025. . This is the zkFOL paper: the semantics, the arithmetisation route, and the soundness contract rest on it. It is the only paper in this list that supports a claim about zkFOL itself. eprint 2025/316. Zinc: Succinct Arguments with Small Arithmetization Overheads from IOPs of Proximity to the Integers. Garreta, Waldner, Hristova, Dall'Ava. CRYPTO 2025. . Third-party work describing the hash-based backend layer this compiler targets. Cited in this documentation only for what the backend is and does. eprint 2026/855. Zinc+: SNARKs for Polynomial Rings. Abdugafarov, Garreta, Kumar, Osadnik, Vesely, Vlasov, Zheng. Nethermind Research with academic co-authors. . Third-party work extending the backend approach to polynomial rings. Cited in this documentation only for what the backend is and does. Citation discipline, stated once for the whole set: the backend papers are evidence about the backend. Their arguments and their benchmarks measure their own constructions on their own hardware, and they are never used in this documentation as evidence for zkFOL's performance, for its position against zkVMs, or for the source of its advantage. Claims of that kind are either measured in-house or grounded in eprint 2024/954. arXiv 2305.09545. Bartoletti, Marchesin, Zunino. Source for the published result that rich contracts, including automated market makers and lending pools, compile onto a predicate chain of this general shape, and for the composition limit this documentation states wherever generality is claimed: cross-contract atomic composition inside a single transaction does not survive the translation. ### Other sources used in this documentation Comparator hardware requirements: RISC Zero zkVM quick-start and local-proving documentation; Succinct SP1 hardware-requirements documentation. Benchmark record: the project's public benchmark harness, containing the code every system ran, the full results tables including serialized proof sizes, the memory methodology, and reproduction steps; zkFOL 0.4.0 against RISC Zero 3.0.5 and SP1 6.3.1 on AMD Ryzen 7 5700X, Linux, measured September 2026, with two backend revisions noted in the record itself. Economics precedents: Ergo storage-rent documentation and parameter-governance record; Cardano ledger documentation for the refundable minimum-value deposit. Mina documentation for its succinct chain proof and its proof marketplace. Market and security figures on the problem page: TRM Labs H1 2026 incident count; DefiLlama Q2 2026; Immunefi H1 2026 loss-category analysis; Procur3 four-year exploit-cost average; Sherlock, Zealynx and Procur3 2026 audit-market references. Solver-paid fees precedent: CoW Protocol production behaviour. The performance tables reproduce from the public benchmark record.