As President Xi Jinping begins his first state visit to the United States, something of a potentially dangerous trend is beginning to emerge in the US-China relationship. There are now a number of influential voices on both sides who believe that the problems in the relationship are so numerous, so profound and so unmanageable that they are starting to overwhelm the post-1972 strategic consensus and are threatening to end a quarter-century of Sino-American goodwill.

The list is formidable. The US sees an increasingly assertive China in both the East and South China Seas, reinforced by an increasingly sophisticated Chinese military. Both the US government and US business are now alive to China’s emerging cyber-capabilities. American business no longer believes it has the same sort of real access to Chinese markets that Chinese firms now have in the US. To this we now add a new scepticism from American business as to the longer-term stability and growth potential of the Chinese economy after a string of troubling economic indicators, and significant stock-market volatility over the summer.

Then there is China’s draft foreign NGO law, which has managed to horrify most American universities, thinktanks and philanthropic institutions that have been active in the People’s Republic. Together, these represent a potent cocktail of American negativity towards the relationship – and that’s even before you add the cyclical lunacy of presidential campaign politics. There are few votes in Washington these days in support of the China relationship.

China’s complaints about US policy are as voluminous as they are visceral. Beijing sees continuing US spy flights along its 12-mile limits as being as diplomatically offensive as they are militarily hostile. It accuses Washington of abandoning its historical policy of neutrality on contested regional maritime claims after America gave its full-blooded support to Japan ruling that its military forces could fight abroad again. The Chinese government denies its culpability for cyber attacks against the US and instead says it is the target of foreign attacks, potentially including the US. China resents its exclusion from an impending Trans Pacific Partnership and sees trade policy as now pulling the region apart rather than bringing it together as in the past.

There is the continued intransigence of the US Senate in rejecting a modest increase in China’s voting rights at the International Monetary Fund, leaving aside the puzzling anomaly that China, as the second largest economy in the world, still has the same voting rights in the Fund as Belgium and the Netherlands combined. And finally, there’s the celebrated case of the Asian Infrastructure Investment Bank, which the US did everything possible to prevent its allies from joining.

Given this growing litany of mutual recrimination, what’s actually in it for both Beijing and Washington to sustain a stable strategic relationship for the future? My argument is pretty simple. First, despite the many difficulties, neither country wants to risk the possibility of conflict, let alone war – neither their governments, nor their populations, nor even their militaries. Second, the mutual economic interests they share (in trade, investment and in financial markets) that would be lost as a consequence of any fundamental strategic implosion of the relationship still far outweigh the economic frustrations they have with each other.

And third, despite all the public sturm und drang on their fundamentally conflicting views of the future of the global order, what these two great powers share is a maximum desire for stability and predictability, in that order. Only in this way can their respective global interests be advanced. Anyone who doubts this need only take a close look at what both Beijing and Washington really think about Islamic State. Or Iran. Or the future of the North Korea nuclear weapons programme. And now even climate change.

If this thesis is true, then the real question for this summit is how to navigate the many shoals of conflicting interests and values that lie ahead. The uncomfortable truth for the growing legions of strategic hawks in both capitals is that the deep disagreements that do exist are solvable. Recent reports of tentative progress in the development of a new joint “cyber-security” regime represent a significant case in point.

But to do that, the two sides need to agree on a new common strategic narrative to govern the future of their relationship. Both their publics need an organising principle that is able to preserve long-term strategic stability, notwithstanding the issues of the day.

There is no particular political magic or diplomatic poetry to this. I have argued for a concept of “constructive realism for a common purpose”: “realism” about managing the real problems in the relationship that are at present politically insuperable; “constructive” insofar as it relates to the much longer and growing list of bilateral, regional and global domains where the two are already cooperating. Then using the diplomatic capital harvested from these constructive projects over time to maximise their “common purpose” in enhancing, not eroding, the current international order.

The coming week will be full of dramatic commentary about why the US-China relationship is in near-terminal condition. If the implicit objective is to contemplate the possibility of sliding into conflict and war, then go right ahead. But if it’s not, it’s time the foreign-policy commentariat on both sides of the Pacific became explicit about how we may actually go about preserving the peace.