Numerical search finds candidate modular-invariant spectra with integer degeneracies for 1 < c < 8/7 and hints at a stronger gap bound near c = 1.
Hellerman,A Universal Inequality for CFT and Quantum Gravity,JHEP08(2011) 130 [0902.2790]
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Descending into the Modular Bootstrap
Numerical search finds candidate modular-invariant spectra with integer degeneracies for 1 < c < 8/7 and hints at a stronger gap bound near c = 1.