Tyre comprising a crown comprising a tread bearing a tread surface, the crown comprising an axially central portion extending over an axial width equal to 50% of the axial width of the tread surface and axially centred over the midplane of the tyre, the axially central portion of the tread comprising at least one deepest cut (74, 76) of the axially central portion of the tread, the crown comprising a crown reinforcement comprising: - a working reinforcement comprising at least one radially outermost working layer of the working reinforcement, the radially outermost working layer comprising metal filamentary working reinforcing elements, - a hoop reinforcement comprising a plurality of textile filamentary hooping reinforcing elements helically wound radially around the working reinforcement and connected to one another by one or more filamentary weft element(s), the hoop reinforcement being arranged radially outside the working reinforcement and radially inside the tread, characterized in that, in the axially central portion of the crown, the mean radial distance E1 between: - the surface that passes through the radially innermost point of the or each deepest cut (74, 76) of the axially central portion of the tread and substantially parallel to the tread surface and - the radially outer surface that passes through the radially outermost points of the textile filamentary hooping reinforcing elements that are radially outermost among the textile filamentary hooping reinforcing elements, is such that E1 ≤ 2.00 mm, and in that the or at least one of the filamentary weft element(s) comprises a plurality of textile monofilaments and/or a plurality of textile fibres selected from organic polymeric synthetic fibres and monofilaments, inorganic polymeric synthetic fibres and monofilaments, and assemblies of these monofilaments and fibres. the crown comprising a crown reinforcement comprising: - a working reinforcement comprising at least one radially outermost working layer of the working reinforcement, the radially outermost working layer comprising metal filamentary working reinforcing elements, - a hoop reinforcement comprising a plurality of textile filamentary hooping reinforcing elements helically wound radially around the working reinforcement and connected to one another by one or more filamentary weft element(s), the hoop reinforcement being arranged radially outside the working reinforcement and radially inside the tread, - a working reinforcement comprising at least one radially outermost working layer of the working reinforcement, the radially outermost working layer comprising metal filamentary working reinforcing elements, - a hoop reinforcement comprising a plurality of textile filamentary hooping reinforcing elements helically wound radially around the working reinforcement and connected to one another by one or more filamentary weft element(s), the hoop reinforcement being arranged radially outside the working reinforcement and radially inside the tread, characterized in that, in the axially central portion of the crown, the mean radial distance E1 between: - the surface that passes through the radially innermost point of the or each deepest cut (74, 76) of the axially central portion of the tread and substantially parallel to the tread surface and - the radially outer surface that passes through the radially outermost points of the textile filamentary hooping reinforcing elements that are radially outermost among the textile filamentary hooping reinforcing elements, - the surface that passes through the radially innermost point of the or each deepest cut (74, 76) of the axially central portion of the tread and substantially parallel to the tread surface and - the radially outer surface that passes through the radially outermost points of the textile filamentary hooping reinforcing elements that are radially outermost among the textile filamentary hooping reinforcing elements, is such that E1 ≤ 2.00 mm, and in that the or at least one of the filamentary weft element(s) comprises a plurality of textile monofilaments and/or a plurality of textile fibres selected from organic polymeric synthetic fibres and monofilaments, inorganic polymeric synthetic fibres and monofilaments, and assemblies of these monofilaments and fibres.