Equation 25 · Part 2 · The Economics and Physical Limits of Running AI Agents at Scale
Symbol n
What this part means
n occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Its job in the formula
n occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Full expression→Symbol n→Article meaning
The passage around this formula
Prompt caching is the documented fix for exactly this, and it is worth being precise about what it fixes and what it does not. Anthropic’s automatic caching, recommended for multi-turn use, places a single cache marker at the end of a request; the system caches everything up to that marker, and the next request’s identical prefix is read from cache rather than reprocessed [ 2 ] . Anthropic’s documentation walks through exactly this pattern for a growing conversation: at each new turn, the system prompt and all prior turns are read from cache, and only the newest exchange is freshly written to cache for next time [ 2 ] . A cache read costs a tenth of the base input price; a five-minute cache…
Learn the underlying idea
A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.
Open the illustrated functions: inputs become outputs guide →
See this notation across published equations →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.