DCRP103 / X72R86: Adjoint Eigen-Lock and Five-Ray Classification

Following the nonlocal tensor-ray eigen-lock kernel left by DCRP102, this round solves it completely at the level of local tensor algebra: diagonalizing the traceless strain S, it proves that every nonzero shear component must satisfy the resonance condition β=s_i+s_j=-s_k, that the diagonal traceless subspace is exactly span{S,C_S^0}, and it gives the complete five-ray spectrum for r=0 (three shear rays plus two coaxial rays); for r≠0 the nonlocal Riesz term loads only the coaxial sector without altering the shear resonance. Using the exact example (S=diag(1,0,-1), Φ=E13, r=0), it proves that the shear eigen-lock can indeed coexist with a nonzero transport–Riesz angular pairing, showing that pure tensor algebra alone cannot complete the proof. The conclusion moves the remaining problem entirely to the global nonlocal self-consistency equation r=T0*Φ (either a coaxial scalar fixed point or one of three shear–Riesz self-consistency systems), leaving the next round to examine the solvability of these nonlocal equations themselves.