This work proposes a minimal dynamical criterion relating attractor behavior in scalar-field cosmology to asymptotic conformal structure. Rather than presenting a complete cosmological model, the paper formulates a structural condition under which attractor solutions approach a radiation-like, effectively scale-free regime (wₑff = 1/3), interpreted as a candidate for conformal asymptotic behavior. Within a flat FRW model with a scalar field and exponential potential, this condition uniquely selects λ = 2, for which the attractor satisfies x*² = 2y*². The result is mathematically simple but conceptually significant, suggesting a non-arbitrary link between attractor dynamics and asymptotic conformal structure. This work is intended as a conceptual note and a minimal research program rather than a complete derivation of conformal cyclic cosmology.
T. P. Chronos (Mon,) studied this question.