Large deviations for sectional-hyperbolic attracting sets

Consider a $C^2$ flow with a general sectional-hyperbolic attracting set and a neighborhood of that attracting set. Let Lebesgue measure be compared with the physical measures, and let the observables be continuous. Sectional-hyperbolic large-deviations conjecture. Large deviations with respect to Lebesgue measure versus physical measures, for continuous observables on a neighborhood of general sectional-hyperbolic attracting sets for $C^2$ flows, should have an exponential upper bound. This would extend the paper's large-deviations result for singular-hyperbolic attracting sets to general sectional-hyperbolic attracting sets; the statement is presented as an open extension.