  We present positivity bounds, derived from the principles of analyticity,
unitarity and crossing symmetry, that constrain the low-energy constants of
chiral perturbation theory. Bounds are produced for 2, 3 or more flavours in
meson-meson scattering with equal meson masses, up to and including
next-to-next-to-leading order (NNLO), using the second and higher derivatives
of the amplitude. We enhance the bounds by using the most general isospin
combinations posible (or higher-flavour counterparts thereof) and by
analytically integrating the low-energy range of the discontinuities. In
addition, we present a powerful and general mathematical framework for
efficiently managing large numbers of positivity bounds.
