Taiji Spherical Geometry Theory (TSGT) provides a systematic analysis of the DHOST Ia class Hessian fivefold degeneracy conditions Q₁–Q₅ by proposing an S² circular Euclidean geometric prototype. A three-stage offline verification (analytical, symbolic, and numerical) strictly confirms: (1) Constant solutions b₁=α and b₂=β identically satisfy all degeneracy conditions; (2) The TSGT S² prototype in 10D extended phase space reduces to Nₚhys=1 (single scalar degree of freedom) via a consistent constraint tower (2 first-class and 4 second-class constraints) ; (3) Numerical stability is maintained at |cₛ²-1|<10^-15 and |ΔH^*|<10^-14. Phenomenological predictions include PTA pulsar timing residuals δτ<10 ns and LISA gravitational wave speed deviation δcgw<10^-15, fully compatible with GW170817 bounds and awaiting 2026 observational verification.
Yi-Wen cheng (Sun,) studied this question.