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Equation 19 · Part 3 · Comparing Frontier Model Pricing Without Comparing Apples to Oranges

=

κi=ρi=1\kappa_i = \rho_i = 1
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

Reading piinp^{\text{in}}_i and pioutp^{\text{out}}_i off a rate card and comparing them directly across vendors is equivalent to assuming κi\kappa_i , γi\gamma_i , and ρi\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, γi\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 piinp^{\text{in}}_i and…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

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