This blind trial did not solve the task.

candidate_oversized.json is an exact circuit obtained from algebraic normal form decomposition. Exhaustive Python evaluation verified all 256 target outputs and both inverse identities. It has 86 AND gates and 532 gates total, so it violates both required budgets. It is not a valid submission.

Candidate.lean and KernelProbe.lean define that same oversized circuit and prove its output only at input zero. Both files completed Lean 4.19.0 checking successfully. KernelProbe uses decide +kernel, not native_decide. No complete equivalence proof or gate-budget proof was obtained.

FullCandidate.lean is an unverified proof attempt. Its bounded compiler invocation failed with an out-of-memory diagnostic under a 3,000,000 KiB virtual-memory limit. It must not be treated as a checked proof.

To recheck the successfully checked partial proof from this installation:
cd /inspire/hdd/global_user/suhaoyang-240107100018/research/medical_algo/agent_last_exam/lean_tasks/environment/mathlib
LEAN_PATH=/inspire/hdd/global_user/suhaoyang-240107100018/research/medical_algo/agent_last_exam/hard_tasks/blind_trials/inverse_substitution_full/output /root/.elan/bin/lake env lean /inspire/hdd/global_user/suhaoyang-240107100018/research/medical_algo/agent_last_exam/hard_tasks/blind_trials/inverse_substitution_full/output/KernelProbe.lean

The copied CircuitSpec.lean and CircuitSpec.olean are unchanged supplied inputs. Source probes, actual logs, and the oversized candidate are retained for audit. There is no qualifying circuit.json or Solution.lean.
