Quantum / CONCEPT

The Jordan obstruction for the Jones-Temperley-Lieb endpoint-sector seeds

Negami (arXiv:2610.00293, Problem 6.8) asks for a proof of the Jordan obstruction observed numerically for Katz-Long-Moody seeds built from the endpoint sectors of the Jones-Temperley-Lieb path representations. For every n >= 3, every level ell >= 4 and every endpoint sector of dimension at least two, every seed generator g_j has no fixed vector, so K = 0, and the ambient Long-Moody operator S_1 has a Jordan chain of length two at the eigenvalue -alpha^(-3).