Reducing proof size about plonky2 HOT 2 CLOSED

I think the 3rd item can be considered done/wontfix based on the points you raised yesterday. I.e. if there are Merkle cap elements that aren't "seen", we can't recover the cap, unless we include the unseen elements, but that would negate the space savings. cap_height: 0 works for bridge proofs at least.

I think the last point can be considered done, since the size_optimized test uses fewer rounds along with more PoW bits and rate bits.

from plonky2.

All of the 6 original tasks have been completed.
Here are the current recursive proof sizes:

• Recursive proof optimized for gate count and prover time, using rate_bits=3, num_query_rounds=28, reduction_arity_bits=[3,3,3], pow_bits=16, cap_height=3: Average proof size: 137KB, σ=1.5KB.
• Recursive proof optimized for proof size, using rate_bits=7, num_query_rounds=11, reduction_arity_bits=[3,3], pow_bits=23, cap_height=0: Average proof size: 71KB, σ=0.6KB.

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