SUPPORT-CONDITIONED RECOVERY AND IDENTIFIA- BILITY IN NEURAL FEATURE SUPERPOSITION

Superposition creates a deceptively simple question: when does a sparse feature dictionary support claims about features rather than merely provide a useful reconstruction? We separate three logically different problems—population iden- tification of feature directions, finite-sample estimation, and coefficient recovery on the supports a representation actually visits. For recovery, we introduce a support-conditioned exact-recovery rate and a computable certificate that exposes both within-support interference and competition from inactive atoms; familiar coherence and Welch criteria emerge only as worst-case corollaries. For identification, fourth-order cumulants determine the dictionary under deterministic Kruskal and generic symmetric-tensor conditions, while Gaussian source subspaces give a concrete non-identifiability mechanism. A global-to-local analysis yields parametric finite-sample accuracy once basin separation and local conditioning hold;departures from independent sources appear as measurable cross-cumulant bias and admit a goodness-of-fit diagnostic. Experiments are organized by what each dataset can actually identify. Controlled support-law sweeps, overcomplete recovery studies, and bottleneck audits show that worst-pair geometry, statistical identifiability,optimizer success, and operational recoverability can move independently. The result is an audit framework whose claims are deliberately no stronger than its observables.