Remove dependency (or automatically enforce it) on constraint counts Nova benchmarks

[huitseeker]

We have tests for constraint counts in Nova: https://github.com/lurk-lab/arecibo/blob/605f89990666cae63ff534245ea701199fe0df82/src/circuit.rs#L462-L502 https://github.com/lurk-lab/arecibo/blob/605f89990666cae63ff534245ea701199fe0df82/src/supernova/circuit.rs#L836 https://github.com/lurk-lab/arecibo/blob/605f89990666cae63ff534245ea701199fe0df82/src/supernova/test.rs#L568

The benchmarks use these constraint counts (see the use of constant NUM_CONS_VERIFIER_CIRCUIT_PRIMARY) and substract it from a target constraint count to estimate performance on a circuit with a certain number of "payload" constraints (the constraint count minus the ones automatically added by Nova's folding verification).

This is brittle and unsafe:

• many changes of the circuits (Supernova and Nova) don't change the benchmarks, when they change the circuit,
• the bench-reported perf becomes inaccurate,
• the bench itself is sometimes dangerous, if the constraint count dips below the constant, the substraction operated in the benchmarks has wraparound semantics (in dev mode) and (attempts to) create gigantic circuits: https://github.com/lurk-lab/arecibo/blob/dev/benches/recursive-snark.rs#L66 (this was fixed in supernova by #253 ).

We should :

• apply the fix of #253 (checked_sub) to the nova bench,
• find a way to keep constraint counts in sync, either by :
  • auto-detecting it, that is computing the augmentation constraint count at bench bootstrapping time, as the test does, or
  • at least having a script/tool checking the bench's constraint count is the same as our tests (for a specific choice of finite field),

[srinathsetty]

The cleanest fix to this will be to write a common routine that does the following. Synthesize a non-trivial step circuit with zero constraints (which the current code in the Nova benchmark supports), run RecursiveSNARK to identify the size of the verifier circuit. The benchmark then use that information to determine the circuit sizes for the benchmark. We will be interested in such a fix in the upstream as well.