Most downstream scripts (e.g. noir-protocol-circuits/bootstrap.sh) call
find-bb, which returns bb-avm by default. Rebuilding only the non-AVM
`bb` target therefore leaves a stale bb-avm and downstream bootstraps
keep failing with the same error after the supposed fix.

…nterface methods

Concrete inputs class for the batched init_3 kernel (three PrivateCallData
fields), exported from @aztec/stdlib/kernel. PrivateKernelProver gains
generateInit3Output / simulateInit3 mirroring the existing init pair.
Generic over N is deferred until a second variant lands.

…ct and VK

Adds PrivateKernelInit3Artifact to the ClientProtocolArtifact union and
to the artifact / VK / VK-index registries. The simulated lookup reuses
the constrained init_3 artifact, since no private-kernel-init-3-simulated
crate exists.

The dynamic-import generator gains a small additive pass that emits
fallback cases mapping <name>_simulated to the constrained <name>.json
for any artifact in artifactsWithoutSimulatedVersions, so lazy and
bundle providers stay in sync (the bundle provider has reused the
constrained artifact for hiding kernels' simulated slot all along).

Adds 'private-kernel-init-3' to ClientCircuitName for stats plumbing.
Adds private_kernel_init_3 to the codegen list so the Noir ABI type
flows through.

Generated files (client_artifacts_helper.ts, types/index.ts, vk_tree.ts)
are gitignored and produced by `yarn generate`.

Adds witness-map converters for the batched private_kernel_init_3
circuit and wires them into BBPrivateKernelProver. Mirrors the existing
init pair; the input mapper matches the Noir ABI for
private_kernel_init_3/main.nr (three private_call_N + three
app_public_inputs_N fields).

When PXE_USE_INIT_3=1 is set and the tx has at least three private app
calls, the first kernel iteration verifies three apps in a single
batched private_kernel_init_3 circuit instead of one private_kernel_init
followed by inners. Saves N-1 prev-kernel HN verifications across the
chain. Falls back to the standard init for txs with fewer than three
calls so the flag can be left on permanently.

Refactors the loop's pop-stack / push-nested / record-step /
build-call-data sequence into a consumeNextApp helper used at every
app-consumption site (top of loop + the two follow-up apps in the
init_3 branch). Total app count is computed once via the existing
collectNested helper.

Leaves a WORKTODO(luke) for the case where init_3 consumed every app
in the tx and the chain can skip directly to reset+tail without an
inner kernel chain.

scripts/reproduce_init3_canary.sh runs a real client_flow with
PXE_USE_INIT_3=1, captures the IVC inputs, proves them with bb (Chonk),
and verifies the proof. Asserts the capture references
PrivateKernelInit3Artifact so a regression in the orchestrator's flag
plumbing is caught at capture time.

Gates the captureProfile expectedSteps check on SKIP_STEP_COUNT_CHECK=1
so the test doesn't abort before writing the msgpack when kernel
batching collapses steps.

The Private-Kernel-Sequencer suite asserts call counts on
proofCreator.simulateInit / .simulateInner with the single-app dispatch
shape (e.g. expect(simulateInit).toHaveBeenCalledTimes(1) and
expect(simulateInner).toHaveBeenCalledTimes(3) for nested calls).

With the new default PXE_KERNEL_BATCH_SIZE=3 the planner routes through
simulateInit2 / .simulateInit3 / .simulateInner2 / .simulateInner3, none
of which have mock return values configured here, so the orchestrator
crashes reading bytecode off undefined. Multi-app dispatch is
integration-tested via the bench captures; this unit suite is about the
single-app orchestration path, so pin the env var locally and restore
it on teardown.

Multi-app kernel batching added 4 new stdlib classes
(PrivateKernelInit{2,3}CircuitPrivateInputs,
PrivateKernelInner{2,3}CircuitPrivateInputs), 4 corresponding
witness-map converters in noir-protocol-circuits-types, and the
BatchPlanner orchestrator helper. Main entrypoint grew from ~1733 KB
to 1760 KB, exceeding the 1750 KB hard limit by 10.72 KB.

Bump to 1800 KB to clear the limit and leave ~40 KB headroom for the
inevitable init_4 / inner_4 work.

…de/integrate-init-3

Cherry-pick of #23092 onto merge-train/fairies. Same flake (`verifies
transactions at 10 TPS` in `tx_stats_bench.test.ts:268`) is now blocking
PRs based on this train; see #23092 for the full analysis (bb.js
NativeUnixSocket backend under 8x parallel IVC verifications
intermittently returning `valid:false`).

Skipping at sub-test granularity keeps the other three serial sub-tests
emitting their compression and single-tx verification metrics; only the
IVC-verifier-under-concurrency metrics are dropped. The
`.test_patterns.yml` flake-retry entry from #23083 stays in place.