This paper investigates the edge structure of fractional quantum spin Hall (FQSH) insulators with half-integer spin Hall conductance. The authors analyze both Abelian and non-Abelian FQSH states, including Pfaffian, anti-Pfaffian, PH-Pfaffian, and 221 FQH states. They find that, under strong spin-conserving interactions, all non-Abelian and Abelian edges flow to a common fixed point consisting of a single pair of charged counter-propagating bosonic modes. When spin-conservation is broken, Abelian edges can become fully gapped in a time-reversal symmetric manner, while non-Abelian edges remain gapless due to time-reversal symmetry and can flow to a new fixed point with a helical gapless pair of Majorana fermions. The study also explores the relevance of these findings to the recent observation of a half-integer edge conductance in twisted MoTe₂. The authors derive an effective theory for the interacting edge of half-integer FQSHs, showing that the edge can be described by a minimal theory with a single non-chiral pair of charged bosons. They also consider the effects of breaking spin conservation and show that the resulting non-Abelian edge can support gapless Majorana modes. The paper discusses the implications of these results for the behavior of FQSH edges in the presence of interactions, and highlights the importance of symmetry in determining the nature of the edge modes. The authors also consider the thermal and electric conductance of the FQSH edge, showing that the thermal conductance vanishes at large system sizes, while the electric conductance is determined by the spin Hall conductance. The study concludes that the edge structure of half-integer FQSHs is highly sensitive to the presence of interactions and symmetry breaking. The results have important implications for the understanding of FQSH states and their potential applications in topological quantum computing. The paper also discusses the relevance of these findings to the recent experimental observation of a half-integer edge conductance in twisted MoTe₂, suggesting that the system may realize a non-Abelian FQSH state with protected gapless edge modes.This paper investigates the edge structure of fractional quantum spin Hall (FQSH) insulators with half-integer spin Hall conductance. The authors analyze both Abelian and non-Abelian FQSH states, including Pfaffian, anti-Pfaffian, PH-Pfaffian, and 221 FQH states. They find that, under strong spin-conserving interactions, all non-Abelian and Abelian edges flow to a common fixed point consisting of a single pair of charged counter-propagating bosonic modes. When spin-conservation is broken, Abelian edges can become fully gapped in a time-reversal symmetric manner, while non-Abelian edges remain gapless due to time-reversal symmetry and can flow to a new fixed point with a helical gapless pair of Majorana fermions. The study also explores the relevance of these findings to the recent observation of a half-integer edge conductance in twisted MoTe₂. The authors derive an effective theory for the interacting edge of half-integer FQSHs, showing that the edge can be described by a minimal theory with a single non-chiral pair of charged bosons. They also consider the effects of breaking spin conservation and show that the resulting non-Abelian edge can support gapless Majorana modes. The paper discusses the implications of these results for the behavior of FQSH edges in the presence of interactions, and highlights the importance of symmetry in determining the nature of the edge modes. The authors also consider the thermal and electric conductance of the FQSH edge, showing that the thermal conductance vanishes at large system sizes, while the electric conductance is determined by the spin Hall conductance. The study concludes that the edge structure of half-integer FQSHs is highly sensitive to the presence of interactions and symmetry breaking. The results have important implications for the understanding of FQSH states and their potential applications in topological quantum computing. The paper also discusses the relevance of these findings to the recent experimental observation of a half-integer edge conductance in twisted MoTe₂, suggesting that the system may realize a non-Abelian FQSH state with protected gapless edge modes.