Recursive1: Per-AIR Normalization (Stage 3)

Recursive1 wraps each Basic or Compressor STARK proof in a SNARK circuit, producing a normalized proof format suitable for tree aggregation.

1. Circuit. A Circom SNARK circuit that verifies one STARK proof. The verification key is selected based on the input proof’s circuit type:

   • Circuit type = “basic”: use the Basic STARK verification key.

   • Circuit type = “compressor”: use the Compressor verification key.

2. Input. One STARK proof \(\pi^{(a)}\) (either Basic or Compressor).

3. Output. A normalized proof \(\pi^{(a)}_{\mathrm{R1}}\) with a standardized output format containing:

   • Public inputs and proof values.

   • The global challenge \(\chi\).

   • The root of the aggregated challenge computation \(\mathrm{rootCAgg}\).

   • The stage1Hash for this AIR instance.