Construct a probability measure reproducing connected spectral correlations

Determine whether a suitable probability measure on the family of fixed-$B$ discrete modular spectra can reproduce the connected spectral correlations associated with torus wormholes.

Background

The fixed-BB construction produces many distinct spectra at the same central charge that share the same perturbative smoothed BTZ entropy expansion. An ensemble interpretation therefore requires additional probabilistic input, namely a measure on this family of spectra. The paper specifically raises whether such a measure can reproduce the connected correlations attributed to torus wormholes, but does not resolve the question.

References

A natural question is whether a suitable measure can reproduce the connected spectral correlations associated with torus wormholes.

— Large gaps and BTZ entropy in modular spectra with positive integer degeneracies  (2609.39930 - Chang et al., 30 Sep 2026) in Section 6, Discussion, paragraph “Spectral freedom and ensemble interpretations”