Non-Local Conditions Buy the Seal with a Parity: A Second Stated Class of Pairing Constructions for Paper #54's Entry 9

Works paper #54's Entry 9 (item D-041-080-22, grade B) at the sharpened price of packet #522 Sec.6 (a)-(c), on the construction horn, by stating and exhausting a second class of pairing constructions -- the class packet #541's scope note named as outside its class B. Gates reproduce, digit-for-digit and in order, both recovered versions of paper #54's Entry 9 price, packet #522's operator and fork exhibits (P^2 = I; handedness flip +0.5 to -0.5; eigenfield seal 0.000000; mixed-parity leak 4.500000; pulse flux 294.3; 24 pairings), packet #535's priced grounds (regularity 9.000000 / 0.000000 / 9.000000; finite energies 4.709563 / 4.290482 / 9.000045; Laplacian eigenvalues 0 / -2.467401 / -9.869604 / -22.206610), and packet #541's class-B exhibits (leak 3|lambda|/2 at k = 3 with samples 0.375 / 0.75 / 1.5 / 3 / 6; sealing set exactly {lambda = 0, Dirichlet}; the datum distinguishes 0 members). The new class N is packet #522's canonical double plus one non-local linear condition imposed at all times: species N1, an integral condition across the scar with one fixed L2 kernel; species N2, a two-point condition coupling the field and its derivative at -a and +a jointly. A condition imposed at all times separates by frequency, so at each wavenumber it is one linear constraint on the mode's two coefficients, while the scar flux of a single-frequency field is (k/2)|A B|. Exhaustion by cases, each exhibited: a non-one-sided frequency leaks singly (kernel exp(x) at k = 3: 72.032981; the two-point condition u(-1,t) = 0 at k = 1: 0.227324); one-sidedness of both kinds at different frequencies leaks across frequencies (kernel cos x + sin 2x: 1.539601); the sealing members are exactly the one-sided-at-every-frequency subfamilies (kernels x^2 and x; the two two-point coefficient families with one constraint coefficient identically zero, verified for k = 1..50), and each admits exactly one parity family of fields -- the parity premise in non-local dress -- and each is an unforced selection, the datum distinguishing 0 of the sampled members. The choice-free bare double leaks. No member of class N meets (a)-(c) together. Disposition: strengthened, not closed; a survivor must come from outside classes B and N or down one of packet #535's priced derivation routes. The sever-instant profile was not worked, derived, characterised, or adopted; the identification route was not worked; producing-count 0, printed. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.