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 commitments — KZG10.
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.