Proposed resolution:

This wording is relative to N5014.

1. Modify [algorithm.syn], as indicated:

   namespace ranges {
     template<bidirectional_iterator I, sentinel_for<I> S, class Proj = identity,
              indirect_unary_predicate<projected<I, Proj>> Pred>
       requires permutable<I>
       constexpr subrange<I> stable_partition(I first, S last, Pred pred,            // hosted
                                              Proj proj = {});
     template<bidirectional_range R, class Proj = identity,
              indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
       requires permutable<iterator_t<R>>
       constexpr borrowed_subrange_t<R> stable_partition(R&& r, Pred pred,           // hosted
                                                         Proj proj = {});
   
     template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
              class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
       requires permutable<I>
       subrange<I>
         stable_partition(Ep&& exec, I first, S last, Pred pred,
                          Proj proj = {});                                   // freestanding-deletedhosted;
     template<execution-policy Ep, sized-random-access-range R, class Proj = identity,
              indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
       requires permutable<iterator_t<R>>
       borrowed_subrange_t<R>
         stable_partition(Ep&& exec, R&& r, Pred pred, Proj proj = {});      // freestanding-deletedhosted;
   }
   

This applies the resolution for US 157-255.