Implication is the relation of entailment between Judgements: if this Judgement, then that one.
Once Meet and Join exist, a new question arises: “under what conditions does one Judgement entail another?” This is not a question about subsumption (Order already handles that). It is a question about conditionality: given that A holds, does B follow? Implication is the answer to this question. Specifically, the Implication A → B is the greatest Judgement z such that the Meet of z and A is subsumed by B. In other words: the most you can say while guaranteeing that, together with A, you get B.
This structure — the greatest z with z ∧ x ≤ y — is residuation. It appears here between Judgements but will reappear later between Flow and Nucleus, governing dynamics and closure. Residuation is a deep structural pattern in the derivation.
Implication forces Negation (implying the bottom — the trivially empty Judgement). The complete structure of Order, Meet, Join, and Implication is a Heyting algebra — constructive logic. This is not classical logic: the law of excluded middle does not hold. Proof of existence requires construction, not merely the refutation of non-existence.