Missing gear vs secret sauce

I want to distinguish between the following two framings:

• missing gear/one wrong number problem/step function/understanding is discontinuous/payoff thresholds: "missing gear" doesn't imply that the last piece added is all that significant -- it just says that adding it caused a huge jump in capabilities.
• secret sauce for intelligence/small number of breakthroughs: "small number of breakthroughs" says that the last added piece must have been a significant piece (which is what a breakthrough is).

I'm not sure how different these two actually are. But when thinking about discontinuities, I've noticed that I am somewhat inconsistent about conflating these two and distinctly visualizing them.

Term	Is the final piece a big breakthrough?	Nature of final piece	Found by humans or found by AI?	Length of lead time prior to final piece	Number of pieces	Explanation
Missing gear	Not necessarily. I think this term is somewhat ambiguous about whether the final piece is expected to be big vs small.
Secret sauce	Yes				Small number, possibly one?
One wrong number function / Step function
Understanding is discontinuous	Not necessarily	Restricts the final piece to be about understanding, where the AI goes from "not understanding" to "understanding" something.
Payoff thresholds	Not necessarily	Does not specify
One algorithm	Yes				Small number, possibly one?
Lumpy AI progress	Yes
Intelligibility of intelligence	Yes
Simple core algorithm	Yes
Small number of breakthroughs needed for AGI	Yes				Small number (up to around 10?)
Good consequentialist reasoning has low Kolmogorov complexity	Yes		I think MIRI wants humans to discover this, for the sake of being able to align the AI. But this core of good consequentialist reasoning can also be discovered by a search process (e.g. resulting in a mesa-optimizer).		Small number?