Three IEP Fixed Points of E8 and Their Stability Hierarchy

We extend the Information-Energy-Phase (IEP) framework of the companion paper (Jeong 2026) to the SO(16) spinor sector of E8, identifying a self-consistent third fixed point τ*s = 0.191890 satisfying S2(τ*s) = log 3. The triple hierarchy τ*g > τ*m > τ*s follows from a universality theorem based on root symmetry. The spinor sector admits a unique self-consistent fixed point under SO(8)-symmetric mean field H* = (1,...,1)/√8, with closed-form partition function Z(v) = ½(1+v)8 + (1−v)8. We establish five results: (i) The spinor fixed point and its closed-form spectrum;(ii) The hierarchy theorem for any simple Lie algebra, with E8-specific ratios ρ1 = 1.8122 and ρ2 = 4.256;(iii) E8 curvature invariants: Ricci isotropy Ric(Hi, Hi) = 60 = 2h∨ for all i = 1,...,8; SO(16) spinor Casimir TrE2/N = 1/4; and Σλ2 = 46 for the Cartan eigenvalues;(iv) The structural origin of Limitation L1 — the IEP mean field HIEP concentrates on the SU(3)fam direction, placing all SU(2)L exotic states at Mthr ≈ MIEP. All corrections examined (perturbative, Kac-Moody, spinor IPT, string cooling) reach at most 35% of the required gap;(v) A spectral action heat kernel factorisation Tr(e−sD2/Λ2) = TrM × Ktotal(τint), with the level-1 E8 Kac-Moody central charge c(E8, k=1) = 248/31 = 8 (exact integer) identifying the IEP E8 lattice with the heterotic string internal CFT. The string-IEP cooling trajectory τ*(N) maps τ*m (at N=0) to τ*s (at N* ≈ 73.6), but the canonical normalisation κ = τ*m/√M1 = 0.030794 places all string states within 6% of MIEP, precluding MZ-scale threshold logarithm generation. All numerical results are verified to machine precision by independent computation. Companion to: "From Non-Existence to the Standard Model: Deriving E8 and Its Physical Predictions from a Single Ontological Axiom" (Jeong 2026).