Agreement-Tested Coordinates: When Named Features Can Support Discovery, and When They Cannot

Interpretability is increasingly used as a discovery tool: an analyst reads a model's named coordinates and treats them as candidate findings about the domain. This inference is only licensed if the names mean something reproducible. We propose two operational criteria that a named coordinate must satisfy before it can support a discovery claim: \textbf{conceptual clarity}, that independent annotators applying the written definition agree at chance-adjusted $\kappa \geq 0.70$, and \textbf{label disentanglement}, that the coordinate does not merely paraphrase the prediction target. We instantiate them in LLM-assisted Feature Discovery (LFD), which proposes lexical and semantic features from outcome-opposed contrastive pairs, screens candidates by cross-LLM $\kappa$, and selects by residual held-out gain. Across ten tasks in seven corpora, LFD has nearly identical observed mean accuracy to a strong text-bottleneck baseline ($0.708$ vs.\ $0.707$ balanced accuracy) while producing markedly more reproducible coordinates. Human evaluation ($276$ raters across the clarity and leakage audits) shows that the clarity gap transfers to people: on a task chosen because its correlation profile \emph{favors} the baseline, independent raters reproduce LFD definitions at feature-median $\kappa = 0.70$ versus $0.11$ for baseline concepts, with two baseline concepts falling below chance. We also report where the criteria fail: compositional tasks where no compact named basis captures the signal, rare features whose $\kappa$ is undefined or unstable, and a measured accuracy cost when disentanglement is certified rather than merely observed. The negative cases delimit when interpretability output is safe to read as knowledge.