This research note records a heuristic conjecture about a coarse dimension pattern for non-round positive Einstein metrics on standard spheres. The note does not claim a proof or a full classification theorem. Instead, it isolates a specific periodic pattern along dimensions divisible by five and places a falsifiable prediction on record. In its current form, the conjecture predicts the coarse sequence ∞, 3, ∞, 0, ∞ at dimensions 5, 10, 15, 20, and 25 respectively, where ∞ denotes infinitely many families of non-round positive Einstein metrics. The pattern is compatible with published results at dimensions 5, 10, 15, and 25. The most informative unresolved test identified in the note is the even-dimensional case S²0. This upload is a public archival version intended for open dissemination and citation. It is a heuristic research note, has not undergone peer review, and is meant as a falsifiable conjectural statement rather than a proof.
Paul Alberto Popescu (Thu,) studied this question.