The Sp(3) Scoring Functional Is Not a POVM Effect

An exact Sp(3)-covariant relational construction stores a single four-index object C_R on a 35-dimensional carrier and reads two different scalars out of it: an induced channel action and a score. The induced action is the trace-preserving map realign(C_R) = L^T, with sector-transfer matrix A_phys = [[1/7, 3/14],[4/7, 6/7]]; the score is the diagonal table A_ext = diag(1/7, 6/7). We prove, exactly over Q(i), three things. First, A_ext is exactly the diagonal of A_phys: the score keeps the sector-preserving coefficients of the induced channel and discards its sector-mixing terms. Second, the operator that produces the score is not self-adjoint — in the standard inner product and in the physical invariant metric G_W its Hermiticity deviations are nonzero (1/14, 3/7 and 3/14, 9/7), and its symmetrized spectrum runs outside [0,1] — so it is not a POVM effect on the carrier. Third, and positively, the same number is a positive figure of merit on the channel: the physical transfer matrix is itself a positive readout A_phys[s,t] = Tr[P_s N(P_t)]/d_s with P_s the self-adjoint (G_W-orthogonal) sector projector, so the score Tr[P_s N(P_s)]/d_s is a nonnegative sector-return fidelity — the trace of two positive operators. The certificate's non-self-adjoint operator merely represents this positive number through the oblique readout M_s = P_s^T = G_W P_s G_W^{-1}, which fails self-adjointness only because [P_s, G_W] != 0. The score is therefore not a measurement effect on states but a positive sector-return figure of merit of the induced CP channel; its non-self-adjoint appearance is a representation artifact of the oblique readout, not intrinsic signedness. All claims reproduce from a standard-library-only Python verifier and a frozen exact-operator file (integrity-checked by SHA-256), with no external dependencies. A naming caveat is stated explicitly: what is established is a G_W-positive sector-return functional, not a process effect or tester in the standard Ziman–CDP sense, which would additionally require standard-metric positivity and a tester normalization not claimed here.