Just when you thought the chasm between what the Kremlin is saying and what it's doing couldn't get any wider, the Russian military reportedly demands that Ukrainian forces surrender while Russian diplomats deny that troops are even in Ukraine.

Exhibit A (CNN):

Ukrainian officials say Aleksandr Vitko, the Russian commander of the Black Sea Fleet, went aboard a blocked Ukrainian warship in Crimea's Sevastopol Harbor on Monday and issued a threat:

"Swear allegiance to the new Crimean authorities, or surrender, or face an attack," he said, according to Vladislav Seleznev, a Ukrainian Defense Ministry spokesman in Crimea who spoke to CNN.

Exhibit B (Twitter):

That's clearly a lie, but it's also clear that Russia doesn't care. State-run television just keeps churning out the justifications:

Mr Kiselev is well known for his anti-Western and homophobic outbursts. In December, a Ukrainian journalist and activist awarded him a mock Oscar for his "lies and nonsense" about the protests in Kiev that eventually led to the ousting of President Viktor Yanukovych.

Denouncing the "bandit excesses" that had brought "democracy to its knees" in Ukraine (language that has now become familiar in Russian TV's coverage of the crisis), Mr Kiselev insisted that Russia had to defend its "interests" and the Russian-speaking population in Ukraine.

"That’s the advantage of Putin’s state-controlled television and his pocket legislature," David Remnick writes in the New Yorker. "You can create any reality and pass any edict."

But should the rest of the world have to live with it?

Remnick compares Russia's move on Ukraine to the Soviet invasion of Prague in 1968 and its invasion of Afghanistan in 1979. But Putin's claims—that Russia has a duty to invade another country to protect a supposedly oppressed linguistic minority, and that the borders of his country should be redrawn to suit him—are also a troubling echo of the ethnic-protection claims made by Adolf Hitler when he grabbed the Sudetenland from Czechoslovakia. (As he said at the time: "I am simply demanding that the oppression of three and a half million Germans in Czechoslovakia cease and that the inalienable right to self-determination take its place.")

And the idea that the world community should abandon Crimea to Putin is beginning to sound like an uncomfortable echo of Neville Chamberlain.

In desperation, Ukraine has started installing oligarchs to control their home regions, apparently hoping that the shared interest of wealth will be a stronger glue to unite them than a politician's abstract notion of national duty.

Chris Collison, writing from Kiev, reports that the mood is calm but tense. Online, people are swapping information about agents provocateurs posing as Russian-speaking Ukrainians pretending to welcome Russian soldiers with waving flags and open arms (Hitler also pulled that p.r. stunt in Sudetenland).

He writes:

Everyone is waiting to see what else the Kremlin has up its sleeve. Ethnic Russians have been protesting outside the Russian Embassy, trying to tell Putin that they don't need his protection. (These have been popping up on social media.)

Elsewhere, Ukrainians are pleading for help from the US and the EU, although it's not really clear what they can do at this point. Maybe they can freeze Russian assets and inflict some economic pain. The ruble took a tumble today, so perhaps financial punishment can provide some leverage. I don't think NATO can get directly involved in this one without causing the situation to escalate beyond control. Russian troops are demanding that Ukrainian military personnel in Crimea disarm, although they have so far politely refused and pledged their loyalty to Kyiv.

He forwarded a video of a Ukrainian officer arguing with Russian soldiers, apparently over who has control of some military equipment and weapons. The YouTube page claims that Russian soldiers moved in on military units and demanded all the weapons, but Ukrainian officers stood in the way, refusing to fight back but also refusing to surrender.

Collison continues:

Meanwhile, the propaganda machine keeps spinning. Yesterday, Russian TV reported that mass numbers of Ukrainians have been fleeing into Russia, although they showed video of cars lined up at the Polish border.

They are continuing the lie that Kyiv is overrun with Nazis and fascists and that only Russia can save the day. There have been reports that Russia is shipping people into the east to wave flags and build its case for moving troops deeper into Ukraine. Two more Euromaidan activists were reportedly beaten to death in the eastern city of Kharkiv last night.

A few days ago, Collison says, some media outlets claimed that a man from Kharkiv climbed up a government building to replace a Ukrainian flag with a Russian one—but Ukrainians believe it's this guy whose Vkontakte (a kind of Russian Facebook) claims he is from Moscow.

"Protesters were identifying Berkut officers [the riot police who shot and killed demonstrators] through Vkontakte when the violence was going on here in Kyiv," Collison writes. "It's interesting how much of this battle is being fought online."

It will also be interesting to see who wins the war over the news—and what, if anything, the rest of the world plans to do about it.