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Equation 9 · Part 7 · How Claude Code's Memory Actually Persists Across Sessions

addition

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}
addition

What this part means

Add the term after the plus sign to the term or group before it.

Its job in the formula

Add the term after the plus sign to the term or group before it.

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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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.