How the most-used zero-knowledge proof system (Groth16) works

In Session 10 of "Proof is in the Pudding," we work backward from Groth16's famously compact verifier equation to explain why the protocol is shaped the way it is. We cover how R1CS constraints become polynomial identities, why pairings are needed to multiply hidden commitments, how random linear combinations and the Schwartz-Zippel lemma enforce witness consistency, and how the separating factors gamma and delta restrict which pieces of the CRS a prover can use.