feat(fnd): real-kernel Chonk flow with an in-app UltraHonk verifier

[iAmMichaelConnor]

Summary

Adds noir-projects/fnd/noir-protocol-circuits/integration-tests/verify-uh-proof-within-smart-contract: a Chonk (ClientIVC) flow over the real private kernels whose app verifies an UltraHonk proof, the way a smart contract does when it verifies a Noir proof in a private function. It is generated entirely from code in this repository (no captured fixtures, no aztec-nr, no PXE), so proving-system regressions in a real kernel stack are caught here without a round trip through the labs repository.

The flow is app_uh_verifier -> private_kernel_init -> private_kernel_reset_tail -> hiding_kernel_to_rollup. The app is a private function as the kernels see one: it emits PrivateCircuitPublicInputs on the return data bus and, on the way, recursively verifies an UltraHonk ZK proof through bb_proof_verification::verify_honk_proof. Until now this path had no proving coverage anywhere: bb's DSL test only checks the circuit and its VK, the stdlib test proves a standalone Mega circuit, acir_tests proves the verifier programs under UltraHonk, and none of the pinned Chonk flows contains an app that verifies a proof.

This also introduces noir-protocol-circuits/integration-tests/ as the home for tests that prove the real protocol circuits end to end with bb, alongside the existing nargo test unit tests and nargo execute fixture runs. See its README.

How it works

• flow-inputs-builder is an unconstrained Noir program that derives every kernel input from the circuits' real verification keys: the VK tree with the kernels at their protocol indices, the app's function tree and contract address, the public data tree non-membership proof for class updates, and the no-op reset hints. It reuses protocol_test_utils::FixtureBuilder and is never proven. The kernel library itself is untouched; the reset hints are built from std::mem::zeroed() plus the documented inactive sentinels, set through the hint structs' public fields.
• prove_uh_verifier_app_with_real_kernels.py (stdlib Python) proves inner_circuit with bb, runs the builder, chains each circuit's return data into the next one's call data with noir-execute, assembles ivc-inputs.msgpack, and runs bb prove and bb verify --scheme chonk. --flow-dir also writes the stack in the chonk-pinned-flows layout, which the existing C++ and bb.js pinned-flow tests accept as-is.
• The test's crates are members of the protocol-circuits workspace (listed in Nargo.template.toml) because nargo always resolves the topmost Nargo.toml. build_integration_tests in the protocol-circuits bootstrap.sh compiles them and moves their artifacts into the test's own target/, so they never reach the protocol artifacts, benches, or pins. The build loop's member grep is tightened to top-level crates/ so it ignores them.
• integration_test_cmds emits two test commands under the existing noir-protocol-circuits-tests target, hashed over the circuits, bb, and the Noir verifier library: the flow must prove and verify, and with --corrupt-inner-proof (one element of the inner proof flipped; ACVM does not check proofs during witness generation) bb must reject it.

Test plan

• noir-projects/fnd/noir-protocol-circuits/bootstrap.sh build_integration_tests, then integration-tests/verify-uh-proof-within-smart-contract/prove_uh_verifier_app_with_real_kernels.py --skip-compile: bb accumulates the four real circuits and the Chonk proof verifies.
• The same with --corrupt-inner-proof: bb fails while building the app circuit, reported as a pass.
• bootstrap.sh test_cmds lists both commands; nargo fmt --check and nargo check are clean; the protocol target/ holds no test circuits after the build.

Not covered yet, as sibling tests to add: multi-call transactions (private_kernel_inner), intermediate resets, and the to-public tail.

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https://claude.ai/code/session_01Dct8Fqzq1WFqckm9vCEbMS