In char 2, a chain lemma makes {a,b,c,d} a well-defined invariant in K4/2K4 that is zero iff a sum of two symbols in K2/2 is congruent to one symbol in K2/4, plus bounds on symbol length for sums of four symbols.
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Sums of two symbols in $K_2(F)/2K_2(F)$ in characteristic two
In char 2, a chain lemma makes {a,b,c,d} a well-defined invariant in K4/2K4 that is zero iff a sum of two symbols in K2/2 is congruent to one symbol in K2/4, plus bounds on symbol length for sums of four symbols.