Equation 25 · Part 3 · The Economics and Physical Limits of Running AI Agents at Scale
Symbol p_out
What this part means
ut is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Its job in the formula
ut is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol p_out→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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.
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Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.