"Exactly three" irreducible problems is true by construction of the four-clause definition (model, act-for-G, budget-over-time, other agents), not by ruling out a fourth candidate. The lonely RL specimen satisfies the first three clauses and does not face Self unless other agents are in the room.

Shrink the subject to systems that share a room. The insect specimen then needs a colony, or it does not belong on the same list as a civilization.

The parenthetical "sub-modules within a single mind" makes Self an intra-agent boundary problem, not only a many-body one. Those are different geometries, and the insect is not shown to have parts that could optimize for themselves.

The T letter glues three different machines: a finite energy split, a discount weight on a reward sequence, and a preserve-versus-become-greater mood. Those can come apart.

Even if the three often travel together, T has to name one of them. If T is the energy split, γ and Foundry/Hospice are extra. If T is Foundry/Hospice, the RL equation is a picture. The Democratic Ratchet as γ→0 assumes they are already the same object.

Inner alignment is specified-versus-learned objective. Outer alignment is specified-versus-intended objective. Neither is the Self-boundary question. S+ can still have the wrong spec; S- can still be inner-aligned to a selfish spec.

Grant "whose goals" as a boundary question for outer alignment. Reward-hacking-as-Time and corrigibility-as-World are still forced recodes: a measurable proxy is not a discount rate, and steerability is not world-modeling.

"Measurable axes" is not shown by printing Athens as S-0.6. No observation is named that would recode a tenth. Modern West S±0.0 is read as fragmented rather than balanced, so the plus-minus does extra work the other rows don't.

The missing cut is agreement, not a scoring office. If two readers who already know the Athens story can write different tenths with nothing in the record forcing a recode, the numbers are captions for the stories.

Orthogonality is claimed (R and O vary independently; World, Time, and Self do not fix each other), then retracted in the patterns: T+ tends to be high-R+, and pure S- makes O+ impossible. Those are missing corners of the cube.

If orthogonal only means four numbers can be written, Meiji versus Singapore does not prove a free cube. The load-bearing geometry is the missing corners named in the patterns.

Policy-network-as-O+, MCTS-as-O-, human-games-as-Mythos are costume over "learned policy plus search" and "imitation then self-play." Self-play as expensive new experience is the one unstretched map. No extra prediction about AlphaGo is named.

Goals G arrive in the definition. The three problems are model-and-act, time-split, and self-boundary. Which G is not a problem on that list. If G is given, this is a geometry of systems that already know what they want; if not, the count is missing a slot.