Equation 17 · Part 2 · Comparing Frontier Model Pricing Without Comparing Apples to Oranges

subscript

p^{\text{in}}_i

subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

Full expressionsubscriptArticle meaning

The passage around this formula

Reading $p^{\text{in}}_i$ and $p^{\text{out}}_i$ off a rate card and comparing them directly across vendors is equivalent to assuming $\kappa_i$ , $\gamma_i$ , and $\rho_i$ are all equal to each other and to 1 across every vendor in the comparison. This article has just shown that one of those three, $\gamma_i$ , genuinely does converge close to 0.1 across all three companies’ published cards — the one term a naive comparison happens to get right by accident. The other two do not converge, are not published as clean multipliers by any vendor, and vary by content type and by task in ways that only measurement on the caller’s own workload can pin down. A price comparison that reports $p^{\text{in}}_i$ and…

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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 →

Sources cited in the article section

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