this explanation text was written by AI

Employee uplift changes the rate of progress, not the horizon directly. The model multiplies the baseline progress rate by 1 + algorithmic share × uplift. The selected curve independently reduces doubling difficulty as the horizon grows; it is normalized so the starting no-uplift doubling time remains 105 days.

Overall time-horizon acceleration is the instantaneous horizon-doubling rate relative to the baseline: baseline doubling time / effective doubling time, or equivalently (1 + algorithmic share × uplift) × starting difficulty / current difficulty. With uplift disabled, the first factor is 1. A value of 3× means a 200% faster doubling rate.

User-supplied confidence intervals use 95%; the fixed 50% algorithmic share has no additional interval. The chart converts all active parameter distributions into nested Monte Carlo outcome bands: brightest for the central 50% of outcomes, medium for 80%, and faintest for 95%.

The chance of infinite horizon uses 10,000 deterministic Monte Carlo draws. Positive parameters use independent, asymmetric log-space distributions; difficulty percentages use independent, asymmetric logit-space distributions. Each distribution is fitted so its lower and upper quantiles match its stated confidence interval. This probability is conditional on those distributions and independence assumptions.

Release dates: Opus 4.5 and Fable 5. Progress rule: Jimfund 2026-VI. Decomposition context: Anthropic RSP v3.1 and Algorithmic progress in language models.