Holding a Philippine flag, Mariel Ipan breaks into tears moments after the Hague-based U.N. international arbitration tribunal ruled in favor of the Philippines in its case against China on the dispute in South China Sea on Tuesday. (Bullit Marquez/Associated Press)

Paul Gewirtz is a professor of constitutional law and the director of the Paul Tsai China Center at Yale Law School.

The authoritative voice of law has now spoken clearly and decisively on a South China Sea churning dangerously with military maneuvers and heated rhetoric. But law’s effects on the conflict are highly uncertain.

On Tuesday, a tribunal at the Permanent Court of Arbitration in The Hague announced a sweeping victory for the Philippines that found unlawful a broad range of Chinese claims and actions regarding the sea. The tribunal’s words vindicate the Obama administration’s admirable search for law- and rules-based answers to foreign policy disputes. Regarding the South China Sea, President Obama has emphasized our commitment to resolving the dangerous conflicts “peacefully, through legal means, such as the upcoming arbitration ruling under the United Nations Convention on the Law of the Sea.”

While this ruling offers a significant positive contribution, law cannot solve all the conflicts in the South China Sea. Tuesday’s decision underscores the limits of law in resolving these disputes in practice, as well as the urgent need to move ahead with negotiations, supported by prudent power politics.

The tribunal’s headline conclusion limits the legal scope of China’s notorious “nine-dash line.” At most, the tribunal said, this line can be a claim to sovereignty over the islands inside the line and maritime rights deriving from those land features as provided under the Law of the Sea Convention. Any pretense that the sea is a Chinese lake has been rejected, though sovereignty issues remain unresolved. Just as significant, and potentially creating more immediate tensions, are the tribunal’s decisions that certain Chinese land reclamations unlawfully infringe on the Philippines’ rights and the Law of the Sea Convention’s environmental rules.

These are major legal conclusions, but they will produce no immediate resolution to the conflict. Despite being a signatory to the convention, China refused to participate in the arbitration and has denounced the decision as “null and void.” China is clearly wrong. But its sweeping rejection reveals the practical limits of law in this context because the tribunal has no enforcement powers — no police force, no sanctions system, no ability to levy fines.

Another fundamental limit is that the tribunal lacks legal power to resolve underlying and potentially explosive conflicts regarding sovereignty over land features, such as the dangerously contested Scarborough Shoal, and disputes over maritime boundaries. And of course no court’s decision can fully address the core geopolitical issues at stake: China’s enormous new capacities, widespread uncertainty about China’s regional intentions, and whether China and the United States can find terms of coexistence in the Asia-Pacific.

So what is the path forward? The United States and other countries should strongly support the tribunal’s judgment as a binding decision in words and deeds. The United States should criticize China’s statements that it will not comply with the tribunal’s conclusions. And it should continue regular freedom-of-navigation operations, taking advantage of any additional navigation rights produced by the tribunal’s decision.

But the Obama administration also must guard against escalation and reach out to other countries for quiet diplomatic discussions of our options. We cannot yet predict China’s range of responses to the tribunal. The possibility exists that a rebuked China will launch new provocations, leading to a crisis that serves no one’s interests — and the United States and its allies must be ready if China seeks to use force to get its way. Additionally, a legally empowered Philippines might ask the United States to use its military to enforce what the tribunal cannot enforce, which would itself create major risks.

Instead, the United States should encourage our Filipino allies — with their legal victory in hand — to pursue direct negotiations with China as the best next step in looking for real-world, peaceful solutions. China has long demanded negotiations, so this is the testing hour for China’s good faith.

Neither country should insist on preconditions to such talks. China should not insist that the Philippines renounce the arbitration award, and the Philippines should not insist that China accept the legal rights awarded by the tribunal. Such demands would doom negotiations before they started. The path of negotiations will be uncertain and difficult. But the Philippines’ position will be significantly strengthened by the tribunal’s award. Negotiations should begin with a focus on lowering tensions, looking for trade-offs and pursuing common development projects, even if ultimate questions of sovereignty are temporarily set aside.

The tribunal ruling will also be wind in the sails of other claimants in the South China Sea. Over time, China might conceivably accept terms similar to those it now denounces if they are the product of negotiations rather than a third-party tribunal. These are all potential contributions of legal rules even when legal judgments are not formally enforceable. Negotiating an enforceable, rules-based code of conduct among the ASEAN nations and China should also be a top priority.

Since the United States has not ratified the Law of the Sea Convention, it is in an awkward position in demanding Chinese compliance. The U.S. Senate should advance ratification as an urgent national security priority. For now, we should try to speak and act jointly with countries that have ratified the convention.

But we have our own national interests and alliances at stake in the South China Sea, and we need to exercise our power and demonstrate our resolve in advancing those. On these fronts, as on others, law will have a role to play, albeit a limited one. Diplomacy backed by power and law is still our best means of helping to shape the future of the Asia-Pacific.