Allen's non-realizability conjecture for unknown pairs of T(2,n)

For an odd positive integer $n$, consider a torus knot $T(2,n)$ and the pairs $(e,h)$ of normal Euler number and first Betti number of smooth surfaces in $B^4$ bounded by $T(2,n)$. The theorem in the source identifies a collection of pairs whose realizability is unknown: if $n\equiv 1\pmod 4$, $(e,h)=(4-2n+2m,1+m)$ for $0\leq m<n-1$; if $n\equiv 3\pmod 4$, $(e,h)=(8-2n+2m,3+m)$ for $0\leq m<n-3$. Allen's non-realizability conjecture. All unknown points in that collection are not realizable. The paper provides counterexamples for $T(2,5)$ and $T(2,9)$, so this conjecture is refuted.