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@@ -1,18 +1,17 @@
-# LAZY SNARK
-### trustless off-chain zk-proof verification
-##Abstract
+# LAZY SNARK: trustless off-chain zk-proof verification.
+## Abstract
 In Ethereum, it is expensive to check zk-proofs on-chain, so we propose to use Fluence to do heavy-lifting off-chain and only go on-chain to challenge incorrect data/proof combination.
-##Why
+## Why
 Let us say, we need to verify zk-proofs in Ethereum smart contract. The problem is that zk-proof verification is a heavy computational task and thus costs a lot of gas. As a result, checking proofs on-chain is not only expensive, but also takes a lot of space in the block. This may lead to serious problems, e.g. in case of mass exit.
-##What
-We suggest checking proofs on Fluence instead. This option does not has gas problem, is much cheaper, but is also trustless. 
-......................................................
-##How it works
+## What
+We suggest checking proofs on Fluence instead. This option does not has gas problem, is much cheaper, but is also trustless.
+
+## How it works
 The process includes the following entities:
--Ethereum smart contract that stores (data, proof) pairs and implements on-chain proof verification. In case the proof is not correct, the smart contract rewards the user who checked this proof with ether.
--Operator who uploads (data, proof) pairs to the smart contract.
--Fluence instance that also implements proof verification, but off-chain. It also stores all the check results.
--Fisherman aka the user of our system. The fisherman wants to find false proofs to check them in a smart contract and get a reward.
+- Ethereum smart contract that stores (data, proof) pairs and implements on-chain proof verification. In case the proof is not correct, the smart contract rewards the user who checked this proof with ether.
+- Operator who uploads (data, proof) pairs to the smart contract.
+- Fluence instance that also implements proof verification, but off-chain. It also stores all the check results.
+- Fisherman aka the user of our system. The fisherman wants to find false proofs to check them in a smart contract and get a reward.
 
 Here is the workflow:
 1. The operator uploads (data, proof) to the smart contract.