In the semi-endogenous AI software R&D model, progress accelerates without bound if and only if returns to software R&D exceed one.
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The differentiator between the fizzle and the SIE is the relative strength of these two effects. Specifically, in a fizzle, each doubling of efficiency requires more than twice as many papers as the last (e.g., from 2 → 6 → 18), implying progress is getting harder at a faster rate than the AGI labor force is improving.
Toy model; later formalized as the condition that returns to software R&D exceed 1.
Under these conditions, a critical threshold emerges: if and only if the returns to research effort exceed unity (\(r > 1\)), the system will exhibit hyperbolic growth and diverge in finite time.
Jones law of motion with fully automated research, E = cA, constant compute.
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