7. Continuation budget math

A continuation’s cost is the newly added context: the Table of Contents plus the handoff note. The invariant that keeps it sane:

tocTokens + handoffNoteTokens  ≤  continuationBudgetRatio × (window − systemPromptTokens)

Measured before the session is created. Over budget → refuse, with per-rule numbers. Never silently truncate.

Why “after the header,” not “of the window”

A 32K model with a ~9K system prompt and tool schemas has only ~23K of headroom. Budget the continuation as a fraction of the whole window and you make it unmeetable on exactly the small-context hardware the plugin exists for. Reserve a share of what remains — here continuationBudgetRatio defaults to 0.25, so on 32K/9K the new content may use ~5.75K tokens, and the TOC that measured ~102 tokens clears it with room to breathe.

Why refuse rather than clip

A dropped or clipped handoff note is precisely the lossy behavior this whole project rejects. A summary can shrink; a citation index should stop short and say so — “TOC + note = 7,420 tokens over an allowance of 5,750 (0.25 × 23,000); trim the note or raise continuationBudgetRatio” — so the human decides deliberately. The same doctrine runs everywhere in the system: offline degrades to local-only naming the failed step; the rules section refuses with its overage and never clips a rule; an oversized tool result whose artifact write fails inlines with the failure named, never silently. Loud beats lossy, every time.

The retention paradox, structurally avoided

In-place compaction has a corner where a message is too big to file and too new to keep — bounded refusal or forced truncation is the usual answer. dsh-chapters makes it unreachable: a monster tool result never enters the window at all — it is stubbed at arrival into artifacts/ (§9), so the retention gate at the rescue stage is instead a never-on-the-desk gate. This is the Recursive-LM decomposition doing bookkeeping for us — next page.

Next: 8. Recursive context theory.