Arithmetization + PCS ⇒ SNARK

Arithmetization together with PCS implies SNARK.

Statement

Migrated verbatim from succinct-argument § Universal/updatable SNARKs:

Systems like Plonk and Marlin use a single universal trusted setup for all circuits up to size , rather than a per-circuit setup. Plonk uses PLONKish arithmetization and KZG polynomial commitmentsKZG10.

Notes

class: unstated: no citing page says which notion of reduction is meant. Recording a class the wiki does not state would add a claim.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

  • Genuinely conjunctive: Plonk needs BOTH an arithmetization and a polynomial commitment scheme.
  • CITATION MISMATCH: KZG10 is the polynomial-commitment paper, not the Plonk paper (GWC19) or the Marlin paper (CHM+20); the systems named in the sentence are uncited.
  • ‘arithmetization’ is a Glossary entry, so a hypothesis slot is filled by a technique rather than a primitive/assumption.