RLCT of the petrol variety for arbitrary table length

Determine the real log canonical threshold of the petrol variety polynomial p_n at every point a in the positive orthant for all integers n greater than or equal to 2, proving that it equals (1, 2) when a lies on the diagonal Δ_n and (1, 1) otherwise.

Background

The petrol variety arises from comparing two calculation paths for estimating average fuel consumption: the correct quotient of the sums of distances and petrol amounts, and the arithmetic mean of the individual distance-to-petrol ratios. For a table with n rows, the discrepancy between these paths is represented by the polynomial p_n in 2n variables.

The paper establishes the conjectured formula directly for n = 2, 3, and 4. It also reports computational evidence that, for n from 3 through 9, the singular locus of the petrol variety within the nonzero coordinate locus is the diagonal Δ_n. Computations for n greater than or equal to 5 were not feasible with the authors' stated computational setup, leaving the general formula unresolved.