The Whole System Pays with a Floor: Complete-System Requirements and Paper #235's Second Door

Works paper #235's second door (item D-220-237-64, grade B) at clauses (a)-(e) word for word, on the second horn, by stating and exhausting a tenth class of requirements -- class X, requirements depending only on the admitted spectrum's complete-system energy set, the set of total energies of systems containing exactly one particle from each admitted orbit, computed from the gated energy ranges by a single Minkowski sum with each support taken once. Gates reproduce the whole body of paper #615's notebook digit-for-digit first (papers #235, #509, #518, #527, #534, #540, #552, #586, #598 and #615's exhibits). Three candidate directions were tested and declined on computed ground before the class was taken: the joint sumset-and-product class (11 joint profiles; it determines both of its components by construction, so the count of pairs sharing a joint profile while the sumset class separates them is 0 -- a conjunction, not a datum distinct in both directions); bounded-order products (the order-at-most-2 attainable-product set equals the full attainable-product set for all 128 admitted sets -- a collapse into class P); and the attainable-difference set (3 profiles, a function of the sumset profile on this table). Paper #615's two declined candidates (resolvent-only and response-only requirements) are not re-presented. Class X is distinct in both directions from all nine exhausted classes, by exhibited pairs against each -- including both directions against the sumset class, whose operation it shares, and against the multiplicative class. The 128 admitted-orbit sets collapse to 6 X-profiles (the whole line absorbing 106); the actual spectrum's X-fibre is printed whole at 8 sets -- 0 negative-admitting, 0 tachyon-admitting, 8 excluding -- exactly the kept-only sets admitting the massive positive orbit, so the strongest member performs both halves of clause (b) at the spectrum P2 returns. The exhaustion is a dichotomy: exactly 3 profiles are clean, their fibres together holding exactly the sixteen discard-free admitted sets, every one bounded below, and the other 3 are dirty; 108 of 120 particle-containing sets share an X-fibre with a discard-admitting spectrum. A class-X 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 an eleventh time, not closed; clauses (a)-(e) unchanged; the exhausted classes now stand at ten. Count unchanged: three postulated inputs, zero derivations. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.