Symbol T_start
arithmetic settled at launch, and every additional CLAUDE.
Read this term in its guide →Published equation contexts
Why this formula appears here
Anthropic ships an interactive walkthrough of a representative session specifically to make this loading concrete, breaking startup context down by component with illustrative token counts: a system prompt around 4,200 tokens, an auto-memory index around 680 tokens, environment information around 280 tokens, MCP tool names around 120 tokens with full schemas deferred until needed, then a global CLAUDE.md around 320 tokens and a project CLAUDE.md around 1,800 tokens in that particular worked example [ 4 ] . The documentation is careful to call these “representative numbers” rather than fixed constants — actual figures move with every project’s own files — but the shape they describe is stable…
Read the representative guide
Symbol T_sys
ys is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol T_mem
em is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol T_env
nv is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol T_tools
ools is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol i
i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Symbol k
k appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Symbol M_i
the token count of the i -th memory file discovered along the walk from the filesystem root to the working directory, summed over however many, k , are found.
Read this term in its guide →Starting index or lower bound: i=1
This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.
Read this term in its guide →Ending index or upper bound: k
This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.
Read this term in its guide →How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 1 · AI Agents & Systems
How Claude Code's Memory Actually Persists Across Sessions
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
Anthropic ships an interactive walkthrough of a representative session specifically to make this loading concrete, breaking startup context down by component with illustrative token counts: a system prompt around 4,200 tokens, an auto-memory index around 680 tokens, environment information around 280 tokens, MCP tool names around 120 tokens with full schemas deferred until needed, then a global CLAUDE.md around 320 tokens and a project CLAUDE.md around 1,800 tokens in that particular worked example [ 4 ] . The documentation is careful to call these “representative numbers” rather than fixed constants — actual figures move with every project’s own files — but the shape they describe is stable…
Meanings in this article
- : arithmetic settled at launch, and every additional CLAUDE.
- : the token count of the i -th memory file discovered along the walk from the filesystem root to the working directory, summed over however many, k , are found.