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Equation 9 · Part 4 · How Claude Code's Memory Actually Persists Across Sessions

Symbol i

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}
ii

What this part means

i 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

i 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

The dollar cost of re-reading the same CLAUDE.md content every turn is close to solved. Anthropic’s prompt caching system lets a stable prefix — system prompt, memory files, tool definitions, anything identical from one request to the next — be written to a cache once and then reused. A cache write costs 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…

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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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