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What is actually known
Three statements about sea moss that hold up without a single marketing adjective.
It is a red alga, and it is a food. Wild sea moss grows on rock in cold, moving water, and people have eaten it in Ireland and the Caribbean for centuries — mostly as a thickener, simmered into puddings and drinks. It is a sea vegetable with a long culinary record, not a recent invention.
It is notable for iodine. Seaweeds concentrate iodine out of seawater and are among the most significant dietary sources of it. Iodine is an essential nutrient. Both of those things are established, and together they are the reason this category needs a serving size and a warning rather than a slogan. The amount in any given jar belongs to that harvest.
It gels because of its carbohydrates. The family of carbohydrates in the cell walls of these algae is why sea moss sets when it cools, and why it thickens a smoothie. It is the same property that put it in Irish kitchens in the first place.
That is the honest inventory. It is shorter than a supplement page and longer than you might expect from a company that could simply have made something up.