Torus-knot singularities and Argyres–Douglas theories: the Huang–Jiang–Oblomkov series as a Macdonald index (numerical observation)

Numerical observation: the two-variable series N_{a,b}(q,t) of Huang–Jiang–Oblomkov for the torus-knot singularities x^a = y^b appears to equal the Macdonald index of the Argyres–Douglas theory (A_{a-1}, A_{b-1}). Checked against BPS-spectrum computations and closed physics formulas for six pairs (a,b); we did not find it in the literature. Offered as a conjecture with evidence; the attached Python script reproduces all checks. Use of AI: the observation, all computations, the literature search and the text were produced by the AI assistant Claude (Anthropic, Claude Opus 5.5) at the request and under the direction of the author, who takes responsibility for publishing it.