Budget sanity: trust the spend tracker over the prompt's stated budget

In a session where the continuation prompt stated one remaining budget (e.g. '$20') but the live spend tracker reported much less (e.g. $8.4), sizing the next task to the tracker figure avoided starting a large formalization (a multi-hundred-line classification theorem) that could not have been finished. Pick a small, self-contained corollary that closes cleanly (build, lint, docs, commit). Record the discrepancy in the handoff notes, so whoever continues doesn't plan around the wrong number.