Comparative Implementation of a Zero-Knowledge Settlement Layer across Five Proof Systems: Design Findings and Measurements

We present a comparative implementation of the same financial settlement circuit in five zero-knowledge proofsystems—Groth16, Halo2/IPA, STARK/FRI, PLONK/KZG, and Nova/folding—and report the design consequencesthat appear only when the comparison is performed on a complete stateful application rather than onmicrobenchmarks.The application is a minimal settlement layer with double-entry value conservation, spending authority, doublespendprevention, threshold issuance, burns, selective disclosure for supervision, and account freezing. Unlikebenchmark suites centered on primitives such as SHA-256, this setting forces persistent state updates, globalinvariants, and multi-authority rules into every backend.We document nine implementation findings absent from typical comparative tables. The most consequential forarithmetization is that AIR lacks native copy constraints, which creates a silent soundness gap when updatingMerkle state unless a lockstep dual-climb pattern is enforced. The most consequential for the application is thatsingle-step settlement discloses the recipient’s balance to the payer, which forced a two-phase transferdesign. We also report identical-condition measurements for setup, proving, verification, and proof size; explainwhy Groth16 was rejected despite superior proof size; and record methodology errors that were detected andcorrected during the work.The reference implementation is public and test-backed. It is not third-party audited and does not implementdistributed consensus. We treat both limitations as part of the result.