The Pairwise Sums Pay with a Floor: Pairwise-Sum-Multiset 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 an eleventh class of requirements -- class Y, requirements depending only on the admitted spectrum's pairwise-sum multiset, the multiset (repetitions kept) of the Minkowski sums of the energy supports over unordered pairs of distinct admitted orbits, one particle from each of two different orbits, computed from the gated energy ranges. Gates reproduce the whole body of paper #627's notebook digit-for-digit first (papers #235, #509, #518, #527, #534, #540, #552, #586, #598, #615 and #627's exhibits). The candidate was taken first in the commission's order of promise and was tested, not assumed distinct: the with-repetition variant of the datum was computed and declined in print (its profile determines the sumset profile on this table -- a refinement of exhausted data, not a distinct datum), and the distinct-orbit datum is distinct in both directions from all ten exhausted classes, by exhibited pairs against each and by exhaustive verification against the eight profile classes -- including both directions against the sumset class, whose operation it shares, against the multiplicative class, and against the complete-system class. The untaken candidates (power sums of one fixed stated order; the ratio set) stand named as directions for a twelfth class. The 128 admitted-orbit sets collapse to 56 Y-profiles (the empty profile absorbing 8 sets; the largest fibre 12); the actual spectrum's Y-fibre is printed whole at 1 set -- the spectrum itself, 0 negative-admitting, 0 tachyon-admitting, 1 excluding -- so the strongest member performs both halves of clause (b) at the spectrum P2 returns, at the smallest fibre in the line. The exhaustion is a dichotomy: exactly 5 profiles are clean, their fibres together holding 11 discard-free admitted sets (the five remaining discard-free sets sit in the empty profile's dirty fibre, since the datum is empty below two admitted orbits), every one bounded below, and the other 51 are dirty; 110 of 120 particle-containing sets share a Y-fibre with a discard-admitting spectrum. A class-Y requirement holding of the actual spectrum either accepts a dirty profile (clause (b) fails) or accepts only clean profiles (clause (c) fails). Disposition: strengthened in pricing a twelfth time, not closed; clauses (a)-(e) unchanged; the exhausted classes now stand at eleven. Count unchanged: three postulated inputs, zero derivations. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.