Conjectural spectral sequence behavior for torus knots T(3,6n ± 1)

Let $T(3,6n+1)$ and $T(3,6n-1)$ be the indicated families of torus knots, and let $E^k$ denote the pages of the link surgery spectral sequence associated to a choice of analytic data and diagram. For each such torus knot, the higher differentials are as shown in the source's figure. Conjectural spectral sequence behavior. For some choice of analytic data and diagram, the spectral sequence converges at the $E^4$ page, and the inclusions on the $E^2$ page extend to the $E^3$ and $E^4$ pages. This is presented as a speculative example intended to illustrate the spectral sequence and suggest a possible pattern for this family; no proof or resolution is supplied.