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Equation 17 · Part 2 · Claude Code, From First Principles: The Agentic Loop, Permissions, and What Actually Executes

Symbol τ

∣ct∣>τ⋅Cmax  ⟹  ct→c^t,∣c^t∣≪∣ct∣.|c_t| > \tau \cdot C_{\mathrm{max}} \implies c_t \to \hat{c}_t, \quad |\hat{c}_t| \ll |c_t|.
τ\tau

What this part means

τ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

τ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

…rather than product description. Treat |ctc_t| as the token size of the context at step t and CmaxC_{\mathrm{max}} as the model’s context limit. Compaction is triggered once accumulated context crosses a configurable fraction τ\tau of that limit: ∣ct∣>τ⋅Cmax  ⟹  ct→c^t,∣c^t∣≪∣ct∣|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…

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