Boundary Conditions Buy the Seal with a Choice: A Stated Class of Pairing Constructions for Paper #54's Entry 9

Works item D-041-080-22 (paper #54, Entry 9) at its sharpened price (packet #522, clauses (a)-(c)) by the construction horn: a stated class of pairing constructions exhausted by computation. Gates reproduce packet #522's exhibits digit-for-digit first (P-squared = I with eigenvalues +1 x3 and -1 x3, det P = -1, the handedness flip +0.5 to -0.5, eigenfield flux at the scar 0.000000 / 0.000000, the mixed-parity leak 4.500000 = k-squared/2 at k = 3, the pulse flux 294.3, and the sealed species' 24 pairings) and packet #535's priced grounds (regularity finite for all test fields; finite energies 4.709563 / 4.290482 / 9.000045; the double's lowest Laplacian eigenvalues 0 / -2.467401 / -9.869604 / -22.206610). The stated class B is packet #522's canonical double plus one local linear boundary condition at the scar, u_x(0) = lambda * u(0), with the Dirichlet condition as limiting member and the bare double as the remaining limit. An exhibited admitted field at wavenumber 3 leaks a largest scar flux of exactly 3|lambda|/2, so the sealing members are exactly two -- lambda = 0 and the Dirichlet limit, both at 0.000000 -- and each buys its seal with an unforced selection choice (the one-sided datum distinguishes 0 members of the family) and admits exactly one parity family of the double's modes: the parity premise in boundary-condition dress. The choice-free bare double leaks. No member of class B meets clauses (a), (b) and (c) together. The sever-instant profile is fenced and was not worked, derived, characterised, or adopted; the identification route was not worked, its uniqueness having already failed on packet #522's record. Disposition: strengthened, not closed; clauses (a)-(c) unchanged; producing test none at present, producing-count 0. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.