The Sums Pay with a Floor: Sumset Requirements and Paper #235's Second Door

Works paper #235's Door two (item D-220-237-64, grade B) at its surviving shape -- clauses (a)-(e) -- by the second horn: an exhaustion of a newly stated eighth class. Gates reproduce, digit-for-digit and in order, paper #235's printed exhibits, paper #509's orbitwise exhaustion (128 admitted-orbit sets, 16 excluding all three P2 discards, 0 exceptions), paper #518's relational exhibits (pair condition 22 of 128 with 6 unbounded satisfiers and all 98 mixed sets violating; ordering condition 8 of 128, the kept spectrum not among them), paper #527's Casimir-and-multiplicity exhibits (72 profiles, 32 flip-fixed, 48 twin pairs, 120 of 120), paper #534's topological exhibits (24 profiles, 120 of 120), paper #540's measure-theoretic exhibits (14 profiles, the actual spectrum's 20-set fibre, 120 of 120 each way), paper #552's spectral exhibits (36 profiles, the actual spectrum's 8-set fibre at 6 negative-admitting / 2 tachyon-admitting / 1 excluding, 120 of 120 on the negative half and 92 of 120 on the tachyonic half), and paper #586's spectral-asymmetry exhibits (12 profiles, the actual spectrum's 4-set fibre at 0 negative-admitting / 2 tachyon-admitting / 2 excluding, 116 of 120 on the negative half and 120 of 120 on the tachyonic half). The new class G is the requirements whose satisfaction depends only on the admitted spectrum's attainable-energy set -- the union of all finite sums of its orbits' energy supports, computed by exact interval arithmetic. The 128 sets collapse to 9 distinct profiles (the whole line alone absorbs 106 sets). The actual spectrum's fibre is 12 sets -- 0 negative-admitting, 0 tachyon-admitting, 12 excluding -- so the strongest member performs both halves of clause (b) at the spectrum P2 returns, the first member of any class in the line to do so. The exhaustion is a dichotomy: the profiles split into 5 clean profiles, realised only by discard-free spectra, every one of whose sets is bounded below, and 4 dirty profiles, each realised by a discard-admitting spectrum; a requirement holding of the actual spectrum therefore either accepts a dirty profile (clause (b) fails) or accepts only clean profiles (it implies boundedness-below, clause (c) fails). Of 120 particle-containing sets, 108 share their fibre with a discard-admitting spectrum. The two candidate classes declined by paper #586 -- scattering phase shifts and spectral flow -- were re-checked against the newest papers #582-#593 and declined again in print: zero hits for scattering, phase shift, spectral flow and deformation; the missing channel and deformation family have not been supplied. Disposition: strengthened in pricing a ninth time, not closed; clauses (a)-(e) unchanged; the exhausted classes now stand at eight; the count of three postulated inputs, zero derivations stands unchanged. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.