Whoever replaces Barack Obama will face many difficult choices but few are likely to be as stark as those in the Asia Pacific region. In a 497-page, densely argued ruling this week, an international tribunal in The Hague blew away the legal ambiguity that has long surrounded China’s claim to control the bulk of the South China Sea — one of the busiest trading routes in the world.

How the White House responds to the verdict in the coming months will help define Washington’s relationship with Beijing for years, and dramatically influence the geopolitics of the region.

Washington sees the ruling, issued by the Permanent Court of Arbitration, after a complaint from the Philippines, as a victory for what some US officials describe as a 21st century rules-based order over China’s 19th-century plans for its own sphere of influence. By rejecting so many of the assumptions that underpinned Beijing’s claims in the South China Sea, the tribunal has put it on the spot.