Tire comprising specified hooping ply

A tire comprising a crown comprising a tread and a crown reinforcement, two side walls, two beads, and a carcass reinforcement,

• each side wall linking a respective one of the beads to the crown,
• the crown reinforcement extending in the crown in a circumferential direction of the tire, the crown reinforcement being radially inserted between the carcass reinforcement and the tread, and the crown reinforcement comprising a hoop reinforcement comprising a hooping ply comprising at least one textile wire-like hoop reinforcer element and a working reinforcement comprising a single working ply comprising wire-like working reinforcer elements,
• the carcass reinforcement being anchored in each of the beads and extending in the side walls and in the crown, and the carcass reinforcement comprising a single carcass ply comprising wire-like carcass reinforcer elements,
• the at least one textile wire-like hoop reinforcer element, the wire-like working reinforcer elements, and the wire-like carcass reinforcer elements being arranged so as to define, in projection on an equatorial circumferential plane, a triangular mesh,
• wherein the at least one textile wire-like hoop reinforcer element has, once removed from the tire, a tangent modulus greater than or equal to 5 cN/tex/% for any elongation greater than or equal to 4% and greater than or equal to 10 cN/tex/% for any elongation greater than or equal to 5%,
• wherein the at least one textile wire-like hoop reinforcer element comprises:
• a core composed of a first strand comprising at least one monofilament;
• and
• a layer comprising at least two second strands, each second strand of the layer comprising at least one monofilament, and each second strand of the layer being helically wound around the core, and
• wherein a sum of stiffnesses in tension at 1% elongation of the at least two second strands is at least 100 times greater than a stiffness in tension at 1% elongation of the first strand.