How ubiquitous is metta as the first training for monastics?

I don’t think this is true. The first ubiquitous instruction in meditation is that which a monk is given during his ordination ceremony. It consists in the asubha practice of recollecting the first five of the thirty-two parts of the body: “head-hair, body-hair, nails, teeth, skin.”

What follows after that varies so much from one monastery to another that nothing at all can really be described as ubiquitous.

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