Prelude: id succ add mul pow. Integers become Church numerals. Application is juxtaposition; \x.body or λx.body for lambda.

Rung is the certified cost class before anything runs. EAL depth = certified elementary tower height; eal:true means the certificate is a real bound (oracle-free safe), eal:false means it abstains.

The linearizer makes every binder affine (single-use) by inserting dup nodes — the same structural discipline that licenses the fast path and bounds cost. κ is the cyclicity warrant on the reasoning shape.

Lower the cap and re-run an exponential/tower term to watch it 💥 detonate (over-space) — source size never predicts this; the cost class does.

Floor-then-gradient: feasible ▸ permitted ▸ best. A plan whose cost class the budget refuses is annihilated to 0̲ — not down-ranked — no matter how high its utility. Cost is a type, and the type decides.