  We propose that the odd-frequency $s$ wave ($s^{\rm{odd}}$ wave)
superconducting gap function, which is usually unstable in the bulk, naturally
emerges at the edge of $d$ wave superconductors. This prediction is based on
the surface spin fluctuation pairing mechanism owing to the zero-energy surface
Andreev bound state. The interference between bulk and edge gap functions
triggers the $d+s^{\rm{odd}}$ state, and the generated spin current is a useful
signal uncovering the ``hidden'' odd-frequency gap. In addition, the edge
$s^{\rm{odd}}$ gap can be determined via the proximity effect on the diffusive
normal metal. Furthermore, this study provides a decisive validation of the
``Hermite odd-frequency gap function,'' which has been an open fundamental
challenge to this field.
