Exact SSUF scenario-count ladder on the four-terminal planar gadget

For the released four-terminal planar acyclic single-source unsplittable-flow gadget, require one unsplittable routing to be no more expensive than a prescribed fractional routing under each of $m$ strictly positive full-demand route-cost-difference scenarios. What is the worst-case normalized additive upper-arc deviation? The v0.3.0 fixed-gadget scenario-count ladder proves $$\beta_G^{(m,+)}= \begin{cases} \dfrac{299-41\sqrt{41}}{32},&m=1,\\ \dfrac{17}{8},&m=2,\\ 3,&m=3,\\ 4,&m\ge4. \end{cases}$$ The $m\ge2$ values are non-attained suprema; no attainment or non-attainment assertion is made for $m=1$. The one-scenario value also holds for legally realizable signed and zero route-cost differences; no such multi-scenario extension is claimed.

Fixed four-terminal planar DAG; positive route-cost differences for m≥2, with non-attained suprema; signed/zero only for m=1, whose attainment is unstated. No topology-wide/unrestricted-planar claim.