Local Hyperbolic Condition for Singular-Guts Invariance

Determine whether Proposition 5.?? on orbit-equivalence invariance of the semiflow on singular guts remains valid without the Local Hyperbolic Condition (LH).

Background

The paper proves invariance of the semiflow on singular guts up to orbit equivalence outside half annuli, and obtains stronger orbit-equivalence invariance when the chosen blowup satisfies the Local Hyperbolic Condition (LH), requiring every closed orbit in the blown-up complex to be pseudo-hyperbolic. The author leaves unresolved whether this additional hypothesis is genuinely necessary.