Time horizon model with employee uplift

Assumptions

Confidence intervals: On Off Use parameter intervals to calculate Monte Carlo bands and ranges.

Confidence level % Applied as the label for every parameter interval below.

AI-progress decomposition: Paper-calibrated Simple 50:50 Derive the algorithmic share from algorithmic-efficiency and physical-compute growth rates.

Paper-calibrated rate decomposition: calculating…

Employee uplift: On Off Applied to the AI-progress rate.

Uplift growth: Linear Exponential Constant percentage growth, extrapolated indefinitely without a ceiling or S-curve.

Exponential growth: calculating…

Difficulty curve: Hill Log-normal Hill: a smooth curve bounded near 100% difficulty at short horizons.

The 105-day baseline is normalized independently at the initial 11.6-hour horizon.

Enter CI bounds to show probability-weighted Monte Carlo bands on the chart. Blank bounds inherit their estimate.

Reset to central estimate

Calculation

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.

The paper-calibrated mode derives the decomposition from empirical growth rates in the paper cited by Anthropic’s RSP. Because compute and algorithmic efficiency multiply, their logarithmic growth rates add, and the algorithmic share is r_algorithm / (r_algorithm + r_compute). The simple 50:50 mode instead reproduces the default algorithmic-share assumption in Jimfund 2026-VI. Anthropic’s RSP does not itself estimate that 50/50 split; its 3× physical-compute × 3× algorithmic-efficiency example is illustrative arithmetic and has no error bars.

The underlying historical pre-training study estimates an algorithmic effective-compute doubling time of 8.4 months (95% CI 4.5–14.3 months) and cites physical training compute doubling roughly every six months. The latter has no CI in this paper and is therefore held fixed unless edited. Its separate algorithm/compute attribution is a Shapley decomposition: algorithmic contributions range from about 4.9% to 40.8% across its listed model pairs, not a single decomposition estimate with a confidence interval. That performance attribution is therefore shown as context rather than substituted for the logarithmic rate decomposition used by this model.

The study covers language-model pre-training from 2012–2023 and explicitly does not estimate post-training gains, employee productivity, or future uplift. Consequently, it informs only the paper-calibrated decomposition; the 50:50 split, uplift anchors, task-horizon baseline, and difficulty curve remain separately labeled scenario assumptions.

User-supplied confidence intervals use the shared confidence level above; the published algorithmic-efficiency interval remains fixed at 95%. 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. In paper-calibrated mode, the paper’s algorithmic-efficiency doubling time is also sampled, and each draw derives its algorithmic share from that sample and the fixed physical-compute rate. 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; paper-calibrated mode also holds the physical-compute rate fixed.

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.