The hx push attribute facilitates the integration of a URL into the browser's history, enabling functionalities such as utilizing the back button seamlessly. This attribute supports deep linking by allowing the handling of both hx requests and standard HTTP requests, which may require distinct processing. Developers must implement logic that distinguishes between these request types, based on the presence of the hx request header, allowing for efficient rendering of either entire pages or specific partials. This approach not only enhances user experience but also maintains predictable navigation and state management within web applications.