plonk(recursion): handle zero public inputs in PI computation and add tests

[Forostovec]

This change fixes a crash in the recursive PLONK verifier when a circuit has zero public inputs. Previously, PrepareVerification unconditionally accessed witness.Public[0], causing an out-of-range panic. We now initialize PI to zero and only sum Lagrange contributions when len(witness.Public) > 0, matching the native backend’s behavior for zero-public-input circuits. A dedicated test was added to ensure recursive verification succeeds with an inner circuit that has no public inputs.

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Note

Handles zero public inputs in recursive PLONK PI computation and adds a test verifying recursive proof with no public inputs.

• Verifier (std/recursion/plonk/verifier.go):
  • Safely compute PI when there are zero public inputs:
    • Initialize pi to 0 and only accumulate ∑ Lᵢ*wᵢ when len(witness.Public) > 0.
    • Adjust lagrange/denom/wPowI progression to avoid out-of-range access.
• Tests (std/recursion/plonk/verifier_test.go):
  • Add InnerCircuitZeroPublic and getInnerZeroPublic helper.
  • New test TestZeroPublicInputsBW6InBN254 validating recursive verification for a circuit with no public inputs (ensures witness.Public is empty).

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[ivokub]

Thanks for the contribution. Indeed, it crashed before. I only added a small change to avoid doing non-native 0+Pi[0]*L_0. It would have taken hot path anyway, but imo a bit cleaner.