At the same time the present work has provided a simple physical understanding/rationalization of the origin and properties of these gaps. We have shown that such excellent agreement can be obtained by a transparent approach, using a minimum of computational resources, avoiding high level many-body methods, such as the advanced GW approach. This is accomplished by recognizing (and suitably exploiting) the fact that most (or all) of the Coulomb correlation energy is devoted to offset the (inversion) symmetry conflict. This is an added insight. Thus, simple DFT calculations with or without "fictitious" open shell states (such as open shell singlets or triplets) can give accurate results, especially when augmented by TDDFT calculation which can further refine the results, provided that the chosen DFT functional includes the "exact" exchange (such as the PBE0 functional used here, proven to provide excellent results ), and the finite length of the AGNRs is taken into account (recall the synopsis of the theoretical approach in section 2.5). Under the same provisions (finite size of AGNRs, and "exact exchange") the GW approach would also give the correct results, as is illustrated in ref. 6, where taking account the finite size of the 7-AGNRs has lowered the GW gap by about 1 eV, in very good agreement with the measured STS value. As a result, a similarly large overestimation of the expected substrate screening would be avoided, since the GW results are widely used as reference values for the free standing AGNRs. This is corroborated by STS measurements of AGNRs on non-metallic substrates. Thus, the measured STS gaps are practically independent of the substrate and virtually equal to the freestanding values, obtained by any of the three computational methods: DFT, TDDFT, and GW (from the simplest to the more complex), provided the finite size and the "exact" exchange are taken into account. Obviously, the simplest (and computationally most economical) approach should be normally preferred, in accord also with Occam's principle. A combination of DFT and TDDFT, as is used here, should be considered ideal.