Rigorous Profiling and Experimentation Plan for a Kernel Simulator

You are given only a kernel simulator that reports cycle counts and microarchitectural counters such as IPC, stall reasons, occupancy, and memory bandwidth. Design a rigorous plan to profile and optimize a compute kernel using this simulator.

Provide:

1. Baseline definition and environment control.
2. Experiment design with controlled variables (including screening vs. deep dives).
3. Data collection schema and derived metrics.
4. Variance reduction and statistical methodology.
5. Stop criteria for iterations.
6. Methods to attribute speedup to specific changes (including decomposition and ablation).
7. Functional correctness checks after each iteration.

Make minimal, explicit assumptions if necessary to ensure the plan is self-contained.