The UPS sign-period conjecture for powers of the infinite Borwein product

Let $c_t^{(m)}(n)$ denote the coefficient of $q^n$ in $(q;q)_\infty^m(q^t;q^t)_\infty^{-m}$, and let a sequence be a UPS sequence when its signs are periodic with a least sign period. The UPS sign-period conjecture. For any positive integers $t$ and $m$, the sequence $\{c_t^{(m)}(n)\}_{n\geq 0}$ is a UPS sequence with least period of sign divisible by $t$.

The result is proved in the paper when $m(t-1)\leq 24$, with explicitly identified exceptional periods; the conjecture extends the asserted periodic sign behavior to all positive integers $t$ and $m$.