Absorbing Shadow Classes in Conjunctive Label Rules

A conjunctive label rule declares an outcome only when a failure condition and an eligibility condition hold together. Where the eligibility condition is absorbing — once false, never true again — units that keep failing become structurally unlabelable, and a residual definition of the negative class absorbs them into it. We call such a subset a shadow class, and the defect is a property of the rule rather than of any instrument carrying one. We give a protocol that detects it before any result exists: a shadow-class census and a learnability gate, both cheap, both pre-registerable, and both evaluated before any detector comparison is computed, so a failure cannot be a post-hoc reading of an unwelcome number. On a MovieLens-25M recommender replay we built, the census finds 69.2% of the nominal control class structurally unlabelable and the gate fails, the most natural early-warning statistic having had its sign inverted. A protocol demonstrated only on its author's own instrument warrants little. We therefore fixed the questions, a seven-branch decision rule and a materiality threshold in advance, hashed and registered them, and applied the protocol to two public instruments we did not build. Both returned negative on the registered hypothesis, with seven further findings reported under evidence grades. Six instruments have now been examined and one carried the defect — the one we built. That is evidence of specificity, not of prevalence: no rate is claimed, and none can be estimated from a selection made on structure.