Negation has no fixed point: no value seats the liar; quarantine is irremovable.

The lazy register is monotone and homes the liar (\(\neg Z=Z\)); the eager register is not monotone: grounding and verdicts require two different registers.

The two-sentence cycle has no eager model over all nine value pairs; the revenge sentence’s content evaluates to \(T\) while the sentence stays quarantined — the price is paid explicitly.

Liar oscillates with period 2, the carousel with period 4; Curry is homeless without using negation; the finite Yablo truncation has a unique grounded model.