Polynomial-time computability of the tent-code bit given rational inputs

Determine whether, for fixed rational μ ∈ ℚ and rational x = p/q, the tent-code bit b_n ∈ {0,1} can be computed in time polynomial in the input size log p + log q + log n.

Background

The authors propose a concrete time-complexity question for computing the n-th bit of the tent code when the initial condition x and parameter μ are rational. While their work addresses space complexity in a smoothed sense, they explicitly state that the existence of a polynomial-time algorithm in the natural input size remains unresolved and note a possible NP-hardness without a known proof.