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where T(t) is the time-horizon at date t and is the empirical doubling period. This is a compact way to state a real, fitted regularity — it is not a physical law, and the paper’s own authors flag that the fit is over a specific task suite combining two internal benchmarks and a small set of newly written short tasks, not over arbitrary production software work, and that the entire extrapolation depends on whether that suite’s difficulty profile actually resembles the tasks an organization needs done. Reading a doubling constant off a fitted curve and projecting it five years forward is a scenario, not a fact; the fact is the fitted curve’s shape over the period actually measured.
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Symbol t
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Equation 9 · AI Agents & Systems
Measuring Claude Code and Agentic Development Tools: Evidence, Benchmarks, and Uncertainty
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
where T(t) is the time-horizon at date t and is the empirical doubling period. This is a compact way to state a real, fitted regularity — it is not a physical law, and the paper’s own authors flag that the fit is over a specific task suite combining two internal benchmarks and a small set of newly written short tasks, not over arbitrary production software work, and that the entire extrapolation depends on whether that suite’s difficulty profile actually resembles the tasks an organization needs done. Reading a doubling constant off a fitted curve and projecting it five years forward is a scenario, not a fact; the fact is the fitted curve’s shape over the period actually measured.
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Equation guide → · Article →Equation 16 · Foundation Models
How Multimodal Models Actually Handle Video, Audio, and Space
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
where is volume density, is emitted colour, and T(t) is accumulated transmittance along the ray up to t . There is no patch, no voxel grid, no fixed token count anywhere in this formulation — the scene is a function evaluated at query points, and any tokenization of it for a downstream language model has to be imposed afterward, by sampling the field at a chosen resolution, which reintroduces exactly the resolution-versus-cost trade video and audio already face.