Equation 41 · Part 2 · The Economics and Physical Limits of Running AI Agents at Scale
superscript
superscript
What this part means
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
Its job in the formula
A raised mark can be a power or an index. Its position and the surrounding notation determine which.
Full expression→superscript→Article meaning
The passage around this formula
Compaction and editing are not free, and the model above shows why they earn their keep anyway. Reset the accumulated history to a small fixed-size summary of s tokens every m steps, and the trajectory becomes a sequence of n/m short quadratic segments instead of one long one: each segment’s own retransmission cost scales with , but the number of segments scales with n/m , so the total across the whole trajectory scales with m n — linear in n for a fixed segment length m , not quadratic. The summarization step itself is not free — reading through a full segment once to compress it costs roughly what one ordinary step near the end of that segment costs — so an interval m chosen too…
Learn the underlying idea
An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.
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Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.