What does this equation mean?

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 $T_p$ tokens reused across n turns of a session, against a per-token base price c , the total cost of that prefix is $\mathrm{Cost}_n = 1.25\,c\,T_p + (n-1)\,(0.1\,c\,T_p) + c\sum_{i=1}^{n} T_{v,i}$. 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 specifically recommended for exactly this kind of content, described in the documentation as “stable, reusable content like system instructions, background information, large contexts” [ 5 ] . In dollar terms, a project memory file that stays identical across a long session is nearly free after its first turn.