Equation 17 · Part 6 · Claude Code, From First Principles: The Agentic Loop, Permissions, and What Actually Executes

subscript

|c_t| > \tau \cdot C_{\mathrm{max}} \implies c_t \to \hat{c}_t, \quad |\hat{c}_t| \ll |c_t|.

subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

Full expressionsubscriptArticle meaning

The passage around this formula

The growth is monotonic and the response is a threshold rule, which is worth writing down because it is the one piece of real mechanism in this section rather than product description. Treat | $c_t$ | as the token size of the context at step t and $C_{\mathrm{max}}$ as the model’s context limit. Compaction is triggered once accumulated context crosses a configurable fraction $\tau$ of that limit: $|c_t| > \tau \cdot C_{\mathrm{max}} \implies c_t \to \hat{c}_t, \quad |\hat{c}_t| \ll |c_t|$ . Concretely, Claude Code “clears older tool outputs first, then summarizes the conversation if needed,” preserving “requests and key code snippets” while allowing “detailed instructions from early in the conversation” to be lost [ 2 ] . This is a lossy operation by design, and what…

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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.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the surrounding passage

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