The Casimir Cannot See the Sheet: Casimir-and-Multiplicity Requirements and Paper #235's Second Door

Works paper #235's Door two (item D-220-237-64, grade B) at its Wave 19 surviving shape -- clauses (a)-(e) -- by the second horn: an exhaustion of a newly stated class. Gates reproduce, digit-for-digit and in order, paper #235's printed exhibits, packet #509's orbitwise exhaustion (128 admitted-orbit sets, 16 excluding all three P2 discards, 0 exceptions), and packet #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). The new class K is the requirements whose satisfaction depends only on the admitted orbits' Casimir-and-multiplicity data (squared mass, Pauli-Lubanski content, per-momentum multiplicity). The two energy sheets of each mass shell share that datum exactly, so the sheet-flip preserves every class-K profile: the 128 sets collapse to 72 distinct profiles (32 flip-fixed sets, 96 in 48 twin pairs), the spectrum P2 returns has a profile-identical twin admitting both negative-energy classes, and 120 of the 120 particle-containing admitted sets share their profile with a negative-admitting spectrum -- no class-K requirement excludes the negative-energy classes while holding of any particle spectrum. The class's member m^2 >= 0 is satisfied by 64 sets and excludes the tachyonic orbit in all of them, yet admits a negative-energy class in 48 of the 64: class K performs exactly one half of P2's joint discard. Disposition: strengthened in pricing a fourth time, not closed; clauses (a)-(e) unchanged; the count of three postulated inputs, zero derivations stands unchanged. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.