General gluing conjecture for real analytic torsion forms

Let $M$ be a smooth fibration over $S$ whose fiber is decomposed along a cutting hypersurface $Y$ into fibers corresponding to $M_{1}$ and $M_{2}$. Let $F$ be a flat vector bundle, and assume that the Riemannian metrics have product structures near the cutting hypersurface. Let $Q^{S}$ be the vector space of real even forms on $S$, let $Q^{S,0}$ be the vector space of real exact even forms on $S$, and let $\chi(Y)$ be the Euler characteristic of $Y$. Denote by $\mathscr{T}(T^{H}M,g^{TZ},h^{F})$ the real analytic torsion form of the fibration, by $\mathscr{T}_{\rm abs}(T^{H}M_{1},g^{TZ_{1}},h^{F})$ and $\mathscr{T}_{\rm rel}(T^{H}M_{2},g^{TZ_{2}},h^{F})$ the torsion forms with absolute and relative boundary conditions, respectively. Let $(\mathscr{H},A^{\mathscr{H}},h_{L^{2}}^{\mathscr{H}})$ be the long exact sequence of flat vector bundles associated with the decomposition, with $A^{\mathscr{H}}=\delta+\nabla^{\mathscr{H}}$, and let $T_f(A^{\mathscr{H}},h_{L^{2}}^{\mathscr{H}})$ be its torsion form for $f(x)=xe^{x^{2}}$.

General gluing conjecture. With the assumption of product structures, the following identity holds in $Q^{S}/Q^{S,0}$:

$$\mathscr{T}(T^{H}M,g^{TZ},h^{F})-\mathscr{T}_{\rm abs}(T^{H}M_{1},g^{TZ_{1}},h^{F})-\mathscr{T}_{\rm rel}(T^{H}M_{2},g^{TZ_{2}},h^{F}) =\frac{\log 2}{2}\operatorname{rk}(F)\chi(Y)+T_{f}(A^{\mathscr{H}},h_{L^{2}}^{\mathscr{H}}).$$

This conjecture addresses an open problem concerning the general gluing formula for analytic torsion forms and higher torsion invariants. The source formulates it as a conjecture; no resolution is stated in the supplied evidence.