A succinct claim on Ethereum is cheap — not because it’s free, but because it’s way cheaper than the alternative.
Here’s why:

With succinct proofs (e.g. zk-SNARKs):

A prover computes everything off-chain

It generates a tiny proof (~10KB)

Ethereum just verifies the proof

Small data. Fast check. Big savings.

Real example: zkSync Era
10,000 transactions processed off-chain.
They generate 1 succinct proof (~10KB) saying:
“These are all valid.”

Ethereum doesn’t recheck each txn. It just verifies the proof.

Cost breakdown:

Proof verification: ~200–300K gas

Calldata (10KB): ~163K gas

Total: ~500K gas
= ~$6.25 at 5 Gwei, $2.5K ETH

Without the proof?
~21M gas = $250+

Savings:
$250 → $6.25
10,000 txns verified in milliseconds
Security = same as Ethereum
This is how zkRollups scale Ethereum

Succinct claim = “This massive thing is valid — here’s a tiny, trustless proof.”

Succinct ≠ free.
But it’s 100x–1000x cheaper than doing it all on-chain.

That's why zkRollups and Validiums are the future of Ethereum scaling.

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Without succinct proofs:

You’d have to post all raw data (can be megabytes)

Ethereum would redo all computation

Cost = millions of gas = $$$

Example: Verifying 1,000 txns directly = slow + expensive