Compressor (Stage 2, Optional)

The Compressor is an optional stage applied when the STARK verifier circuit for a particular AIR exceeds $2^{17}$ rows.

1. Circuit. A Circom circuit over the Goldilocks field that verifies one Basic STARK proof. The circuit’s execution trace forms a new AIR.

2. When needed. If the number of verifier circuit rows is \(\leq 2^{17}\), the Compressor is skipped and the Basic proof proceeds directly to Recursive1.

3. Output. A new STARK proof \(\pi^{(a)}_{\mathrm{Comp}}\) with a smaller verification circuit than the original Basic proof.

4. stage1Hash. The Compressor computes a commitment hash:

   \[ \mathrm{stage1Hash}^{(a)} = \Poseidon\bigl(\mathrm{vk}^{(a)},\; r_1^{(a)},\; \mathrm{airValues}^{(a)}\bigr), \]

   which chains through subsequent recursive layers.