What does this equation mean?

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 survives it is uneven rather than uniform: a project-root CLAUDE.md is re-read from disk and re-injected after compaction, while nested CLAUDE.md files and path-scoped rules are not re-injected automatically and only reload the next time a matching file is touched [ 6 ] . The practical upshot — stated by Anthropic as a workaround, which is itself evidence of the failure mode it is a workaround for — is that persistent instructions belong in the project-root file rather than in conversation, “since detailed instructions from early in the conversation may be lost” otherwise [ 2 ] . A context window, in other words, is not a growing record of everything that happened; it is a budget under active, lossy management, and the compaction boundary is one of the more consequential pieces of unglamorous engineering in the whole system.