feat: GKR Add Instance

[Tabaie]

• Change the GKR API so that defining the circuit and assigning instances are separated. It removes the necessity of defining hints for the output and deferred "finalize" functions.

• Remove the Println function in favor of GetValue.

• gkrgates.Register now checks if a gate of the same name has already been registered. If so, it compares the gates and returns an error if they are not equal. If they are equal, it returns false, nil.

• Remove all logic pertaining to reordering of wires and instances.

• Unless the user explicitly provides their own initial challenge, automatically use all input and output of the circuit as initial Fiat-Shamir challenge.

• Rename GkrCompressions to GkrPermutations to correctly reflect its function. (Note: a future PR should implement compressions instead and revert the name change)

• A benchmark for gkr-poseidon2

---

Note

Revamps GKR with Compile/AddInstance API and default Fiat–Shamir challenge, adds a reusable hints engine wired into solvers, and hardens gate registration and codegen across curves.

• GKR API:
  • Introduces API.NewInput, API.Compile (returns *Circuit), and per-instance Circuit.AddInstance; removes old Solve/Println paths.
  • Adds Circuit.GetValue (debug), automatic padding, and default initial Fiat–Shamir challenge (commitment to inputs/outputs) unless provided.
• Solvers/Hints:
  • New gkrhints engine (GetAssignment, Solve, Prove) and solvers now override these hints for all curves.
  • Generates solver_hints.go and gate_testing.go per curve; fixes MulAcc to multiply.
• Gate Registry:
  • gkrgates.Register options validate exclusivity, support per-gate curve allowlists, detect and compare duplicate registrations, and expose EqualGateFunction checks; updated tests.
• Internal Types/Utils:
  • Simplifies gkrinfo.StoringInfo (removes dependency/print logic); CircuitInfoToCircuit sets NbUniqueOutputs and validates curves.
  • Adds helpers (SliceOfRefs, ExtendRepeatLast) and exports ComputeLogNbInstances.
• Poseidon2 GKR:
  • Renames to GkrCompressor, builds circuit via new API, and adds RegisterGkrGates.
• Examples/Tests:
  • Updates all examples and tests to new API (per-instance, default FS, GetValue), adds new benchmarks; removes legacy hint/test paths.
• Docs:
  • Fixes package doc name for log-derivative lookup.

^{Written by Cursor Bugbot for commit dec4b30. This will update automatically on new commits. Configure here.}

[cursor]

Bug: Intermediate wires not padded in finalize

The padding logic only extends input and output wire assignments to the next power of 2, but intermediate wires are not padded. This creates an inconsistency because the ProveHint calls repeatUntilEnd which pads all wires including intermediate ones. The mismatch between frontend and hint padding could cause the GKR proof verification to fail or produce incorrect results when intermediate wire values are accessed after padding.