Kanade and Russell conjectured three Rogers–Ramanujan-type partition identities modulo nine in 2014. In Kurşungöz's double-sum form they equate three double sums with infinite products, and they had remained unproved for over a decade.

Bilinear identities are derived for a related series G in terms of the sum-side series F, using q-difference equations. A Casoratian determinant of auxiliary series built from q-Airy functions is evaluated. A theta-function connection formula then yields a cubic norm identity N(A,B,C) satisfied by the sums. The products satisfy the same cubic identity, proved with theta-function addition formulas. Tsuchioka's coefficientwise inequality and a positivity lemma for the cubic norm then force the sums and products to be equal.

All three symmetric Kanade–Russell identities modulo nine are proved, as formal power series and as holomorphic identities on |q|<1. The proof was developed with AI assistance. The identities were also formalized in Lean 4 by GPT-6 Astra based on this proof.