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Equation 9 · Part 1 · How Claude Code's Memory Actually Persists Across Sessions

Symbol n

Costn=1.25 c Tp+(n−1) (0.1 c Tp)+c∑i=1nTv,i\mathrm{Cost}_n = 1.25\,c\,T_p + (n-1)\,(0.1\,c\,T_p) + c\sum_{i=1}^{n} T_{v,i}
nn

What this part means

n appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Its job in the formula

n appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

The passage around this formula

…a documented 1.25 times the base price of an input token; a cache read, on every subsequent turn that reuses it, costs a documented one-tenth of that base price [ 5 ] . For a stable prefix of TpT_p tokens reused across n turns of a session, against a per-token base price c , the total cost of that prefix is Costn=1.25 c Tp+(n−1) (0.1 c Tp)+c∑i=1nTv,i\mathrm{Cost}_n = 1.25\,c\,T_p + (n-1)\,(0.1\,c\,T_p) + c\sum_{i=1}^{n} T_{v,i}. where the final sum covers each turn’s own variable content. Past the first turn, every further read of the same CLAUDE.md content costs a tenth of an uncached read — caching is…

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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