DCRP104 / X72R87: Riesz Self-Consistency and the Shear-Polarization Survivors

Following DCRP103's five-ray eigen-lock classification, this round imposes the nonlocal self-consistency condition r=T0*Φ on each ray, and proves that the whole-space L² eigen-lock of the frozen-simple-strain coaxial branch is identically zero (the Frozen Coaxial L2 NO-GO, whose exceptional set is a measure-zero quadric cone), so the coaxial node is thereby completely excluded. By contrast, a single shear ray still has nonzero whole-space L² solutions off the resonance cone, and axisymmetric strain is structurally less rigid still: its two-dimensional shear eigenspace can produce an infinite-dimensional r=0 polarization kernel. It further proves that under fixed positive viscosity, every frozen constant-coefficient eigen-lock is identically zero. The conclusion notes that Riesz self-consistency alone cannot close the case: the survivor splits into three branches — a shear zero-order-transfer branch, a near-resonance concentration branch, and an axisymmetric polarization branch — leaving the next round to examine whether these surviving branches can maintain their spectrum in the vanishing-viscosity limit.