Adverse authority is found by searching for the rejection, not the rule.

Lawyers rarely miss adverse authority for lack of effort. They miss it because they searched for the wrong thing. They searched for their rule. Opposing counsel will search for the exception to it, and the two searches return different cases.

A query for authority on a rule retrieves cases stating and applying the rule. A query for authority on an argument, the specific inference from rule R applied to facts P yielding conclusion C, retrieves something else: the decisions in which a court considered that inference and declined to draw it. That second body of law is the negative space of the argument, and it is where the opposition's research memo is already written.

Three searches attached to every load-bearing rule find much of it. Search the exceptions directly, in the language courts use for carve-outs. Search the cure paths: how losing parties in the same posture got a second chance, through leave to amend or a request for more discovery. Search the distinguishing cases: every decision that cited the lead authority and refused to apply it. For the argument itself, restate it as a single proposition and search it joined with rejection language in the forum.

For legal AI, negative space is a representation requirement, not a prompt. A corpus that indexes only holdings cannot answer "which courts rejected this argument," because rejected arguments were never recorded as objects. Negative-space ignorance is one of the structural failure categories of document-level systems, and more retrieval does not cure it. The disclosure duty in Model Rule 3.3(a)(2) turns on what the lawyer knows. This search is how the lawyer comes to know it.