Remember, remember: this is about the whole of Ukraine, not just Crimea. Vladimir Putin knows that. Ukrainians know that. As the reported killing of a Ukrainian soldier shows, there is nothing the government in Kiev can do to restore its control over Crimea. The crucial struggle is now for eastern Ukraine. If the whole of Ukraine, including the east, participates in peaceful, free and fair presidential elections on 25 May, it can survive as one independent country (minus Crimea). It will also be back on an unambiguously democratic, constitutional path. In everything the EU and the west does over the next two months, that should be our first priority.

Only the criminally naive or the hardened fellow-traveller could maintain that the pro-Russian groups now working to produce chaos, disorientation and violence in cities such as Donetsk and Kharkiv are not actively supported by Moscow. In Tuesday's New York Times there was a fine eyewitness account of one such stage-managed demo in Kharkiv. At the base of a giant Lenin statue, a huge banner read: "Our homeland: USSR!" As the reporters pointed out, this was all made for Russian television. Whatever Putin finally decides to do, the media narrative will be prepared: whether for an escalating intervention or, as he would undoubtedly prefer, to blackmail the whole country back into the Russian sphere of influence.

It would be equally naive, however, to pretend that there are not real fears among many in eastern Ukraine. Start by abandoning the labels "ethnic Ukrainians" and "ethnic Russians". They mean almost nothing. What you have here is a fluid, complex mix of national, linguistic, civic and political identities. There are people who think of themselves as Russians. There are those who live their lives mainly in Russian, but also identify as Ukrainians. There are innumerable families of mixed origins, with parents and grandparents who moved around the former Soviet Union. Most of them would rather not have to choose. In a poll conducted in the first half of February, only 15% of those asked in the Kharkiv region and 33% around Donetsk wanted Ukraine to unite with Russia.

In the same poll, the figure for Crimea was 41%. But then take a month of radicalising politics and Russian takeover, with Ukrainian-language channels yanked off TV. Add relentless reporting on the Russian-language media of a "fascist coup" in Kiev, exacerbated by some foolish words and gestures from victorious revolutionaries in Kiev. Subtract Crimean Tatars and Ukrainians living in Crimea, who largely boycott the referendum. Season with a large pinch of electoral fraud. Hey presto, 41% becomes 97%.

It is not just Russian "political technology" that changes numbers and loyalties. What happens in such traumatic moments is that identities switch and crystallise quite suddenly, like an unstable chemical compound to which you add one drop of reactant. Yesterday, you were a Yugoslav; today, a furious Serb or Croat.

So everything that is done in and for Ukraine over the next weeks and months must be calculated to keep that identity-compound from changing state. Shortly before President Putin's amazing imperial rant in the Kremlin on Tuesday, another speech was broadcast on a Ukrainian TV channel. Speaking in Russian, the interim Ukrainian prime minister, Arseniy Yatseniuk, said that "for the sake of preserving Ukraine's unity and sovereignty" the Kiev government is prepared to grant "the broadest range of powers" to the mainly Russian-speaking regions in the east. This would include giving cities the right to run their own police forces and make decisions about education and culture.

That was exactly the right thing to do. Now he and his colleagues should go to these places, and say it again and again – in Russian. They should support Russian as an official second language in these areas. They should not dismiss talk of federalisation simply because Moscow also favours it. They should actively want there to be a pro-Russian candidate in the presidential election. And they should do everything they can to ensure that election is free and fair, including diversified media coverage in Russian and Ukrainian – unlike the vote in Crimea.

The west in general, and Europe in particular, can support this in numerous ways. The OSCE, EU and other international organisations should flood the place with election monitors. Western governments must make sure Ukraine's authorities have the money to pay the bills right now. Political parties and NGOs can send advisers. The west can also up the ante. It can make the medium- to long-term economic offer of relations with the EU more attractive. It can threaten Moscow with sanctions far worse than those currently imposed, not just if Putin takes his marked or unmarked forces anywhere else in eastern Ukraine, but if he keeps on trying to destabilise it by proxy.

The time has also come to talk turkey with Ukrainian oligarchs such as Rinat Akhmetov, who is as powerful as any state institution in eastern Ukraine. Quietly but firmly they must be shown carrot and stick: a rosy future for your businesses in the world economy if you help Ukraine survive as an independent, self-governing state; financial strangulation and endless court proceedings if you don't. (One of the eastern oligarchs, Dmitro Firtash, has already been arrested in Austria on an FBI extradition request. It's all about an investment project back in 2006, they say; nothing to do with current politics, you understand.) If Putin's Olympic sport is hardcore wrestling, we cannot confine ourselves to badminton.

None of this is to suggest that what has happened in Crimea does not matter in itself. In his Kremlin speech, Putin scored a few telling hits on US unilateralism and western double standards, but what he has done threatens the foundations of international order. He thanked China for its support, but does Beijing want the Tibetans to secede following a referendum? He recalled Soviet acceptance of German unification and appealed to Germans to back the unification of "the Russian world", which apparently includes all Russian-speakers. With rhetoric more reminiscent of 1914 than 2014, Putin's Russia is now a revanchist power in plain view.

Without the consent of all parts of the existing state (hence completely unlike Scotland), without due constitutional process, and without a free and fair vote, the territorial integrity of Ukraine, guaranteed 20 years ago by Russia, the US and Britain, has been destroyed. In practical terms, on the ground, that cannot be undone. What can still be rescued, however, is the political integrity of the rest of Ukraine.

Twitter: @FromTGA