Ratio conjecture for spin and ordinary Chiodo integrals

Prove that the ratio of the coefficient of degree $2g-1$ in the genus-$g$, zero-point spin-parity Chiodo class $Omega_{g,0}^{pm}(t)$ to the corresponding coefficient in the ordinary Chiodo class $Omega_{g,0}(t)$ equals $b_g^{pm}/b_g$; equivalently, establish that the degree-$2g-1$ coefficient of the genus-$g$, one-point ordinary Chiodo class satisfies $[t^{2g-1}]Omega_{g,1}^{1}(t)=(-1)^g(2^{2g-1}-1)2^{-g}lambda_glambda_{g-1}$.

Background

The paper compares spin-parity Chiodo classes with ordinary Chiodo classes through Segre-class identities and uses known volume formulas to determine ratios of certain integrated spin and non-spin expressions. The authors then formulate a stronger coefficient-level assertion for the degree-$2g-1$ terms of the relevant Chiodo classes.

The conjecture is motivated by numerical evidence and, in genus $3$, is related to the minimality of the Chiodo class under the established low-genus Gorenstein property. The paper does not prove the assertion in general, so it is an explicitly unresolved problem rather than a result used merely as an intermediate claim.