What is the best way to hold a sphere and for how long?
In my experience, spheres done with the reverse method (calcium solution dipped in alginate) can last up to four days, well refrigerated, and kept submerged in vegetable (soy or canola) oil. I do not know the science behind it, only that it works. For reference, these were spheres made of a carrot-ginger consomme, not certain of specific amounts of calcium chlorate (in the carrot mix) and sodium alginate (bath) used. Note that acidity may play a role in how long spheres will last, and (often) the chemical reaction will continue, albeit slower; on Day 1 we'd have thin membranes with very liquid interiors. By Day 4, the membrane would be perceptibly thicker and the contents more glutinous.