Wow, I'm blown away by Holden Karnofsky, based on this post alone. His writing is eloquent, non-confrontational and rational. It shows that he spent a lot of time constructing mental models of his audience and anticipated its reaction. Additionally, his intelligence/ego ratio appears to be through the roof. He must have learned a lot since the infamous astroturfing incident. This is the (type of) person SI desperately needs to hire.

Emotions out of the way, it looks like the tool/agent distinction is the main theoretical issue. Fortunately, it is much easier than the general FAI one. Specifically, to test the SI assertion that, paraphrasing Arthur C. Clarke,

Any sufficiently advanced tool is indistinguishable from an agent.

one ought to formulate and prove this as a theorem, and present it for review and improvement to the domain experts (the domain being math and theoretical computer science). If such a proof is constructed, it can then be further examined and potentially tightened, giving new insights to the mission of averting the existential risk from intelligence explosion.

If such a proof cannot be found, this will lend further weight to the HK's assertion that SI appears to be poorly qualified to address its core mission.