The Ratio Set Has No Clean Reading: Ratio-Set Requirements and Paper #235's Second Door

Works paper #235's second door at clauses (a)-(e) word for word, on the second horn, by stating and exhausting a thirteenth class of requirements -- class AA, requirements depending only on the admitted spectrum's ratio set Rat(S): the merged union, over ordered pairs of distinct admitted orbits, of the interval quotients of their energy supports {E/E' : E' != 0}, closures taken, in the predecessors' interval arithmetic extended to division (sign-split parts, corner limits, 0 never a divisor). Gates reproduce the whole body of paper #640's notebook digit-for-digit first (papers #235, #509, #518, #527, #534, #540, #552, #586, #598, #615, #627's candidate declinatures and class-X exhibits, #636's with-repetition declinature and class-Y exhibits, and #640's candidate splits and class-Z exhibits). The candidate was taken last in paper #636's printed order of untaken candidates (pairwise sums #636, power sums #640, ratio set here) and was split by computation before it was taken: the free-closure ratio set (the attainable-energy set divided by itself) carries 3 profiles and is a function of the sumset profile on all 128 sets -- declined as a coarsening of an exhausted class; the self-pair ratio set carries 3 profiles and is likewise a function of the sumset profile -- declined; the definite-energy ratio set (ratios of the rest energies +1, -1, 0 alone) carries 4 profiles and is a function of the spectral profile on all 128 sets -- declined; the pairwise ratio multiset carries 32 profiles and determines the ratio set over all pairs -- declined as a refinement on paper #627's standard. The set form is distinct in both directions from all twelve exhausted classes, by exhibited pairs against each and by exhaustive verification over all pairs against the ten profile classes and the power-sum class. The 128 admitted-orbit sets collapse to 5 ratio profiles: the whole line at 92 sets (78 negative-admitting, 62 tachyon-admitting, 0 excluding), (-inf, 0] at 12 (12 / 0 / 0), [0, inf) at 10 (2 / 0 / 8), {0} at 6 (2 / 1 / 3), and the empty set at 8 (2 / 1 / 5). The actual spectrum's own profile [0, inf) is dirty -- its fibre of 10 sets holds the negative-admitting sets {massive negative, massless negative} and {vacuum, massive negative, massless negative}, the two negative orbits divided by each other giving only nonnegative ratios -- and, the headline, NOT ONE of the 5 profiles is clean: every ratio profile is realised by a discard-admitting spectrum, so every class-AA requirement holding of any spectrum fails clause (b) there, a requirement accepting only clean profiles holds of nothing, and the dichotomy's clause-(c) horn is empty (clause (c) is never reached). 120 of 120 particle-containing sets share a ratio fibre with a discard-admitting spectrum. Disposition: strengthened in pricing a fourteenth time, not closed; clauses (a)-(e) unchanged; the exhausted classes now stand at thirteen; and the door's named-candidate supply ENDS with this class -- the item carries at its price with the supply's end printed. Count unchanged: three postulated inputs, zero derivations. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.