# Serialize `self` to JSON using the `to_s` representation of each item
	fun to_thin_json: String
	do
		var thin_poset = new POSet[String]
		for e in self do
			var from = (e or else "null").to_s
			for g in self[e].direct_greaters do
				thin_poset.add_edge(from, (g or else "null").to_s)
			end
		end
		return thin_poset.serialize_to_json
	end