'Empirical claims are at the heart of Christianity.' Events in Christ's or Christian history can be looked at, I am happy to hear you imply, in the light of continuing observation of similar phenomenon and their interpretation. Empirical science requires that one repeat an event and see how outcomes change in association with varying inputs, something rather difficult with the Resurrection.
A rabbi said that one of the oldest prayers is 'May the face of God shine upon you.' A book 'The Hidden Face of God' develops the idea that new religions emerge as a sense of the face of God being unrecallable or distant occurs. Marxism can fall into that view. A recent Wall Street Journal article remarks that what Adam Smith called civil society, capitalism in the Marxist critique, empiricaly gives better outcomes for the poor, viz. all the Mexicans in the U.S., than a statist or Marxist society. Yet Marxism, as recently promoted by Eva Morales in Bolivia, surely persists because it brings an experience of the face of God to people with ideas of 'brotherhood,' 'fairness,' e.g. those damn rich men not getting their camels through the eye of a needle, and 'from each according to his means,' which is necessary in a family. All in all a present Messianism which, for some, represents the face of God and which can have some empirical validation by Pres. Chavez delivering free food and medical care (from nationalizing oil resources).