Why it is a question
THEORY-185 now states, as a theorem, what follows when each binary attribute of a word affects its co-occurrence independently and multiplicatively. The PMI then has rank at most d + 1 with eigenvectors affine in the attributes, so its spectral embedding gives parallelograms exactly. The source infers that real co-occurrence is close to this form from the shape of the PMI spectrum and of analogy accuracy against dimension, and those are shapes the model was built to match. No attribute, strength or dimension is recovered from data.
What would answer it
For the word quadruples of analogy families, a measurement of how far the PMI departs from additivity in the attributes across all context words, finding that families close to additive are the ones a spectral embedding completes and those far from it are not, would answer it yes. So would an intervention on a corpus that adds an interaction between two attributes (contexts that favour one combination beyond the sum of the two effects), with that pair’s parallelogram breaking in the PMI embedding while the others stay. Families that the embedding completes although their PMI is far from additive would answer it no. What cannot settle it: more agreement in the shape of analogy accuracy against dimension, or of the PMI spectrum.