?? "restoring unique factorization" to "square-base pyramid" /ad=bc ... ???? not fit "chemistry analogy" story so far as i can see yet ... ??? what were my ideas about this (...) ?? ... ???? ?? or did i just somehow overlook it (...) ?? .... ???? ... ?? seems would be pretty silly to overlook it ... ??? 2d vs 3d ... ????? .....

?? 2*3 = (1+5i)*(1-5i) ????? ..... ??? ...

?? .... ?? dependence on nothing more than x tensor Q+ .... ?????? .....

?? 2d intuition ... ?? intersection of all "snug free envelopes" .... ???? .... ??? messed up in 3d .... ??????? ...... ?????? .....

?? so what _does_ happen in Q(sqrt(-5)) ???? ..... ????? ..... "x tensor Q+" .... ???? .....

??? dedekind ....ideals modulo principal ideals ..... ????? .....

??? maybe it really does always (?? .... dedekind ... ??? ...) happen that the multiplicative monoid is (roughly ... essentially ... ??? ...) smug in an orthant .... ???? ...... ??? .... ??? comm monoid of principal ideals as snug in comm monoid of ideals ..... ????? ...... ??????? ..... ?????? .... or not ????? ......

?? case where "universal orthant envelope" clearly doesn't exist ???? ...... ???? ....

?? maybe ... ??? need certain degree of "non-singularness" (??? ...) before game of "unwrapping with ramification only at ..." makes sense ?? .... ????....