3.7k HP. Unbuffed, out of party.

2 Armor pieces of Allagan (Gloves, Headgear), AF+1 Body (Cleric's Robe) and Relic+1.
I came across a WHM in a titan party today who had 4k and was wearing darklight, but the person pretty much sacrificed all their accessories to be Vitality ones - and some crafting ones to slot in a bit of Vit.

As much as the 3.5k HP thing is a safety net, it shouldn't be required. I've said it a hundred times before but there's been plenty of healers who've beaten Titan HM with 3k HP alone, including myself on my first completion.