An organization that’s developing a backcountry network of huts along 180 miles of trails in Maine’s western mountains is holding a ribbon-cutting ceremony to celebrate the opening of the fourth of 12 lodges that are planned on the trails. Maine Huts and Trails says the public is invited to the ceremony on Wednesday at its new Stratton Brook Hut in Carrabassett Valley. The hut, which opens to lodgers on Dec. 21, is Maine Huts’ first lodge in an alpine setting, with views of Sugarloaf Mountain and Carrabassett Valley. It has 10 rooms and sleeps up to 44 people. So far, Maine Huts has developed 50 miles of trails with three huts, each of which has a main lodge, rooms with beds, hot showers and home-cooked meals.