What does this equation mean?

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 $m^2$ , but the number of segments scales with n/m , so the total across the whole trajectory scales with m $\cdot$ 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 short pays that overhead too often, and one chosen too long lets the quadratic term inside each segment grow large again before it is cut. Anthropic’s own reasoning behind sub-agent summaries, returning one to two thousand tokens rather than a full working transcript [ 6 ] , is exactly a statement about keeping s small relative to m , which is what makes the reset worth performing at all rather than merely deferring the same bill.