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FRI folding

FRI folds an evaluation vector in half: the challenge β combines the even and odd parts into a codeword over a domain half the size. A codeword of degree below d collapses to a single repeated constant after log₂ d folds and stays constant under further folds. A codeword of higher degree generally does not collapse within those log₂ d folds, but an exceptional challenge can flatten it: with d = 2, one fold of X³ at β = 0 gives zero. The degree-8 codeword below collapses at no β in 𝔽₉₇. On a larger domain, folding it further would eventually flatten it too, which is why the fold count is fixed by the degree bound rather than read off the result. Slide β over all of 𝔽₉₇ and watch one fold, all a degree bound of d = 2 requires, of the chapter's degree-1 polynomial against a fixed degree-8 codeword.