The functions c32rtomb and mbrtoc32 from <cuchar>/<uchar.h> are described in the C Unicode TR (draft) as performing conversions between UTF-32¹ and "multibyte characters".

(...) If s is not a null pointer, the c32rtomb function determines the number of bytes needed to represent the multibyte character that corresponds to the wide character given by c32 (including any shift sequences), and stores the multibyte character representation in the array whose first element is pointed to by s. (...)

What is this "multibyte character representation"? I'm actually interested in the behaviour of the following program:

#include <cassert>
#include <cuchar>
#include <string>

int main() {
    std::u32string u32 = U"this is a wide string";
    std::string narrow  = "this is a wide string";
    std::string converted(1000, '\0');
    char* ptr = &converted[0];
    std::mbstate_t state {};
    for(auto u : u32) {
        ptr += std::c32rtomb(ptr, u, &state);
    }
    converted.resize(ptr - &converted[0]);
    assert(converted == narrow);
}

Is the assertion in it guaranteed to hold¹?

¹ Working under the assumption that __STDC_UTF_32__ is defined.