Why it is a question
Every from-scratch number behind THEORY-117 is the best checkpoint as scored on the unseen combinations, by the authors’ design. That makes the failures under more volume strong evidence and the successes an upper bound. The volume test is one architecture, n = 3, k = 1, up to four times the data (sixteen on two datasets). The classifier half of the paper’s Proposition 4.1, and how either half degrades when factorization is only approximate, are also open. Until 2026-10-20 this was THEORY-117’s promote_when.
What would answer it
The volume-against-diversity comparison repeated with model selection on a validation split disjoint from the unseen combinations, so that a model never chosen by its score on the test pairs still fails under more data of the same combinations and succeeds as coverage rises; a second architecture trained from scratch, or more than two concepts, would widen it. The account is refuted if, at fixed coverage, enough added data of the seen combinations closes the gap on unseen ones, or if networks reach high accuracy on unseen pairs at low coverage without linearly factored features. Further runs with oracle selection cannot settle it.