Self-consistent inflationary trajectory in the Triptyque Conceptuel: n_s=0.9649, spectral closure, and modified tensor-to-scalar consistency relation

DESCRIPTION — NOTE V10 This companion note provides a concise self-contained summary of the three central results of Triptyque Conceptuel version 10 (DOI: 10.5281/zenodo.19389437). (i) The inflationary background equation of motion σ_NN + (3−ε)·σ_N + V’/H² = 0, where V(σ) = Ω²(σ)·[T_Q + m²σ²], admits a universal slow-roll attractor independent of the initial condition σ₀. On this attractor, n_s = 1 − 6ε_V + 2η_V = 0.9649 at N = 57.1 e-folds before the P10 threshold (Λ = 4), compatible with the Planck 2018 measurement (0.9649 ± 0.0042). (ii) The constraint P_s = 2.1×10⁻⁹ (Planck 2018) fixes the unique free parameter of the model: m_phys = 1.585×10⁻³ M_Pl and T_P10 = 7.924×10⁻⁴ M_Pl. The model is thereby reduced to zero free parameters once P_s is imposed. (iii) A modified tensor-to-scalar consistency relation is established: r = κ_phys = 3·m²_phys = 7.5×10⁻⁶, differing from the standard slow-roll result r = 16·ε_V = 0.140. The Triptyque prediction is compatible with current bounds (r < 0.034, 2025 datasets), whereas the standard value is not. The modified relation r ≠ −8·n_t (with n_t = −0.0175) constitutes a falsifiable prediction in principle testable by future CMB polarisation experiments. The central open question for version 11 is the formal derivation of the canonical perturbative variable z in the effective geometry g_eff = Ω²(σ)·η.