Trial began at 2026-10-15 04:58:26 UTC, deadline 05:18:26 UTC. Only copied task input files were inspected for the mathematical problem; no reference or authoring content was read. Process-status inspection for memory monitoring incidentally displayed unrelated compiler command-line paths, but no source or circuit data from those paths was opened.

Both bytes are permutations. Each has degree seven. Their differential distributions do not match a single affine-equivalent field inverse. No affine byte relation under XOR input translation was found. Searches involving canonical field/AES inversion, modular affine maps, and small reversible Toffoli transformations did not identify a compact implementation.

The retained circuit uses a six-variable ANF basis and two-variable expansion, with shared XOR subexpressions. All 28 choices of the two expansion variables were tested. The best total count was 936 gates, including 106 AND gates. A separate Python evaluator checked all 256 outputs exactly.

The initial unbounded monolithic Lean run was stopped voluntarily when RSS approached 1.3 GiB after a shared-memory resource warning. The proof was split into separate input lemmas. Lean's -M argument caused an unknown max_memory option error in this installation, and a 2 GiB virtual-address limit caused a segmentation fault even while compiling CircuitSpec. The final check instead uses an external monitor that terminates the compiler above 1,536,000 KiB RSS. The compilation result is reported in result.json and lean.log.

Final result: chunked CircuitData.lean compiled successfully and its well_formed theorem has no axioms. Full equivalence compilation was stopped before the deadline. Both circuit budgets are violated; the trial is not solved.
