Equation 6 · Part 1 · How Claude Code's Memory Actually Persists Across Sessions
Symbol T_p
What this part means
the number of tokens.
Its job in the formula
is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol T_p→Article meaning
Where the article explains it
For a stable prefix of tokens reused across n turns of a session, against a per-token base price c , the total cost of that prefix is
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 tokens reused across n turns of a session, against a per-token base price c , the total cost of that prefix is
Learn the underlying idea
A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.
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Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.