0_6699 Ultraclean, nominally metallic carbon nanotubes upon suspension always display a residual intrinsic gap at the charge neutrality point. The residual, intrinsic gap is thought to have a many-body origin, associated with either a Mott¹ or an excitonic phase² . The two scenarios are fundamentally different as a Mott phase¹ is driven by the short-range part of the Coulomb interaction, while an excitonic phase² is originated by the long-range part of the Coulomb interaction. Despite the two phases being characterised by different symmetry properties, an exhaustive experiment is still lacking.Here we show that the distinctive feature of the excitonic insulator phase is the presence of a cusp in the dispersion of the gap with the axial magnetic field, close to the gap minimum. On the contrary, the Mott phase exhibits a featureless, rounded profile. The non-analytic spike originates from the extreme sensitivity of electon-electron interactions to the Aharonov-Bohm gap modulation. This is demonstrated on the basis of a model for screening³ developed by us adapt for tubes of different size and chirality, capable to replicate first-principle computations of the electron-electron interaction in nanotubes.¹Deshpande et al. Science 106 (2009)² Island et al. Phys. Rev. Lett. 121, 127704 (2018).³ Sesti et al. Phys. Rev. B.105 195404 (2022)