Proposed resolution:

This wording is relative to N5014.

1. Modify [algorithm.syn], header <algorithm>, as indicated:

   […]
   template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
            class Proj = identity, class T = projected_value_t<I, Proj>>
     requires permutable<I> &&
              indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
     subrange<I> remove(Ep& exec, I first, S last, const T& value,
                        Proj proj = {}); // freestanding-deleted
   template<execution-policy Ep, sized-random-access-range R, class Proj = identity,
            class T = projected_value_t<iterator_t<R>, Proj>>
     requires permutable<iterator_t<R>> &&
              indirect_binary_predicate<ranges::equal_to,
                                        projected<iterator_t<R>, Proj>, const T*>
     borrowed_subrange_t<R>
       remove(Ep&& exec, R&& r, const T& value, Proj proj = {}); // freestanding-deleted                                     
   […]
   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>
       remove_if(Ep& exec, I first, S last, Pred pred, Proj proj = {}); // freestanding-deleted
   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>
       remove_if(Ep& exec, R& r, Pred pred, Proj proj = {}); // freestanding-deleted
   […]
   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>
       partition(Ep&& exec, I first, S last, Pred pred, Proj proj = {}); // freestanding-deleted
   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>
       partition(Ep&& exec, R&& r, Pred pred, Proj proj = {}); // freestanding-deleted
   […]
   

2. Modify [alg.remove] as indicated:

   […]
   template<execution-policy Ep, random_access_iterator I, sized_sentinel_for<I> S,
            class Proj = identity, class T = projected_value_t<I, Proj>>
     requires permutable<I> &&
              indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
     subrange<I> 
       ranges::remove(Ep& exec, I first, S last, const T& value, Proj proj = {});
   template<execution-policy Ep, sized-random-access-range R, class Proj = identity,
            class T = projected_value_t<iterator_t<R>, Proj>>
     requires permutable<iterator_t<R>> &&
              indirect_binary_predicate<ranges::equal_to,
                                        projected<iterator_t<R>, Proj>, const T*>
     borrowed_subrange_t<R>
       ranges::remove(Ep&& exec, R&& r, const T& value, 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>
       ranges::remove_if(Ep& exec, I first, S last, Pred pred, Proj proj = {});
   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>
       ranges::remove_if(Ep& exec, R& r, Pred pred, Proj proj = {});
   

   -1- Let E be […]

3. Modify [alg.partitions] as indicated:

   […]
   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>
       ranges::partition(Ep&& exec, I first, S last, Pred pred, Proj proj = {});
   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>
       ranges::partition(Ep&& exec, R&& r, Pred pred, Proj proj = {});
   

   -1- Let `proj` be `identity{}` for the overloads with no parameter named `proj`.

The P3179R9: Parallel Range Algorithms paper was accepted to C++ working draft for C++ 26. Unfortunately, there is an oversight for three algorithms — `remove`, `remove_if` and `partition` — where the `permutable` constraint is missing. This applies to "Iterator and Sentinel" overloads only. The issue exists in [algorithm.syn] as well as in per-algorithm sections: [alg.partitions] and [alg.remove].