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Equation 7 · Part 1 · Frontier AI Model Comparisons: A First-Principles Introduction

Symbol s_obs

sobs=atrue+δcontam+εconfig,s_{\mathrm{obs}} = a_{\mathrm{true}} + \delta_{\mathrm{contam}} + \varepsilon_{\mathrm{config}},
sobss_{\mathrm{obs}}

What this part means

any observed score.

Its job in the formula

sos_obs is part of the quantity the equation computes from the expression on the right.

Where the article explains it

A slightly more general way to see the same point: any observed score can be written as

The passage around this formula

…inflation term from training-set overlap, and εconfig\varepsilon_{\mathrm{config}} is noise contributed by harness, prompt, effort level, and grading choices, which can push the observed score in either direction. Two systems’ sobss_{\mathrm{obs}} values can differ substantially even when their atruea_{\mathrm{true}} values are identical, and can appear equal even when their atruea_{\mathrm{true}} values are not, purely through the other two terms. Nothing about this requires bad faith on anyone’s part; it follows from the measurement…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.