How do we measure where the law is genuinely unsettled?

Ask a research tool whether the discovery rule applies to ERISA limitations claims and it may answer yes, cite real cases, and never mention that other circuits hold the opposite. Nothing in that answer is fabricated. It is worse than fabricated: it presents a contested question as settled. The Institute's work on determinacy starts from a distinction most legal AI never draws. Shallow ambiguity is a research gap: the law exists, and more research will find it. Genuine ambiguity is a feature of the law itself: courts have reached opposite conclusions, or the answer turns on a term, a principle, a method, a jurisdiction or an analogy that competent judges read differently. No amount of searching resolves the second kind, and a system that cannot tell the two apart will smooth the second into the first.

This program treats determinacy as something to measure rather than assume. The Grayness Score grades how contested a question is from the structure of the authority, using a five-type taxonomy of genuine indeterminacy: semantic, normative, methodological, jurisdictional and analogical. Ariadne's Thread goes a step further. Instead of building Dworkin's Hercules, the judge who finds the one right answer, it seats a panel of posture-instantiated judge-agents over the same verified materials, has each score a procedural motion gate by gate, and reports Z: the dispersion between postures, net of a replicate noise floor. A low Z says the outcome does not depend on who decides. A high Z says it does, and shows where. The method's claims about the world are stated as conjectures with refutation tests, and the whole program is conditional on a calibration experiment named in advance.

Why this matters: a lawyer who knows whether a question has one path or many advises, settles and chooses a forum differently. A legal AI system that reports uncertainty honestly is obeying the Zeroth Law of system design, which forbids unwarranted confidence. And a court or reviewer who can see where discretion, rather than law, is doing the work can contest that choice in the open. Ariadne gives a thread, not a verdict.