Is it safe to have 4V continuously supplied to a lithium battery?
I am interested in the answer to this question and, while I have read much on LiIon batteries, I have not seen it answered with certainty anywhere or addressed directly.

I agree with the intuitive logic of Ignacio's answer, but I think that he is probably incorrect in practice. 


Practical information supplied to me by an experienced manufacturer of battery powered products is that the general experience of Chinese manufacturers of LiFePO4 based products is that LiFePO4 cells, which are similar but not identical in general chemistry to Lion, will degrade and die if constant float voltage is applied to them. LiFePO4 cells would if anything be expected to be more robust and resistant to adverse treatment than LiIon (due to the Olivine internal matrix which resists the mechanical degradation mechanisms which LiIon suffers from.)
It is generally advised that use of a lower terminal constant voltage will increase LiIon cycle life at the expense of lower absolute capacity per charge-discharge cycle. However, ALL LiIon charging algorithms and chargers that I have seen terminate the charge cycle at some point and remove the charge voltage. ie they never "float" the battery. Less aggressive chargers terminate charging when Ichg is say 50% or 25% of Imax, and more aggressive chargers charge until Ichg dropsto say Imzx/10, but none ever let Ichg trickle off to zero.


As allowing Ichg to drop to some very low value would maximise capacity and simplify charging it would seem logical that manufacturers would do this if it was acceptable. None do, that I have ever seen.   

LiIon battery manufacturers all advise a minimum end of charge current.   

Charger IC manufacturers typically offer several end of charge currents but none ever offer "float" as an option. 

So, it seems highly likely based on the above, that floating a LiIon battery will cause premature degradation.