I think the cold stratification may not be too exacting in application. I'm judging just by what comes up under the pawpaws in my yard. Also the seeds sprouting in my rotating compost tumbler. That doesn't get regular additions, just when I have something I've been processing and think it's something the worms in there might like. Friend Marianne says "sugar". It's mostly worm castings at this point, I might put some shredded sticks in if I think it's getting too moist. Fall time comes there will be pawpaws that I didn't get distributed before getting past the point of enticing, then parings from friends persimmon harvest, that sort of thing. I seem to never get it half emptied out to utilize the good stuff, so maybe my observation of random ignored seed germination, pawpaw we're talking about, has to be tempered with a richly nutritive growing medium in the composter after all.  I do give the composter a minimum three turns maybe two or three times a season. As that goes the sprouting rootlets get a little convoluted directionally, trying to find which way is up. Pretty sure they are not trying to sense toward or away from the light as its dark in there, but they ARE, majorly, growing around in curls. Might be interesting to see what they might grow into, form etc. But it won't be me, I'm not allowed to bring home any more trees or plant roots of anything that might get larger than a small shrub. The seedlings under the mature trees are growing in native clay soil that I'm finally starting to mulch with shredded pruning materials from around the yard, apples pears, camillias. Stratified as they sit on the soil in the normal run of the seasons. Of course none of these either in dirt or in composter were ever allowed to dry out. Probably some roots in the composter could be two years or maybe older as well as the newer ones that are no doubt coming along now.   By the way, if you are local and would like to try your hand at growing out any of these pawpaw sprouted seeds and I conjecture they may be conducive to transplanting at least as well as any coddled seedlings.. oh, snap! Anyway, reach out if you want some. No charge of course. Parents are Wilson and Mango.