Table A4. Institutions and scale

Symbol Definition
F(τ) ≔ Pr(iτ), τ ∈ ℝ+ Distribution of instruction-environment quality across an institution’s episodes: the share of episodes whose quality is at least τ; non-increasing in τ (§6).
F′ Distribution after an upward shift; first-order stochastic dominance, F′ (τ) ≥ F(τ) for all τ ∈ ℝ+; the considered shift of §6, not a standing assumption (§6).
cmax The most a user will spend in an episode; the user is admissible when cmin (i)≤ cmax (§6).
S > 0 Execution scale: more compute, more parallel attempts, longer runs (§7.1).
R(S) The outcome at execution scale S; the gate conditions of §5 are read on R(S) (§7.1); production set out in Appendix B.1.