Legal openness is measurable as noise-corrected dispersion across lawful judicial postures over fixed, verified law.

The usual question in legal AI is whether a machine can decide a case. Ariadne's Thread asks a narrower question that can actually be answered: how open is this one? Openness, on this definition, is the portion of a disposition that changes when the judicial posture changes and the legal materials do not.

The method follows from the definition. Fix a verified legal substrate, so that every reasoner works from the same good law. Declare a panel of posture-conditioned reasoners, each a stable filter over the same admissible moves, differing in how readily it ends cases, where it prefers to screen, how much fact development it allows, and how it resolves contested process questions. Have each posture score a defined procedural gate on a constrained scale, and replicate each posture to estimate the instrument's own noise. Z is the between-posture variance minus the noise floor, normalized by the largest variance possible on the scale, so that it lies between zero and one.

Two features make this a measurement rather than a forecast. It needs no history of decided outcomes, so it can be computed for a single new motion. And it contains no reference value for the correct disposition, so arguments about who is right operate on a channel the metric does not read. A positivist can read a high Z as discretion the law leaves to the judge; a Dworkinian can read it as a sign that the instrument has not found the best interpretation. The number is the same.

The formal properties of Z are true by construction. Whether real postures separate, whether the substrate is faithful at scale, and whether Z tracks the openness experts recognize are stated as falsifiable conjectures, not results.