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κ_R = 1 − √κ_R = 1/Φ² ≈ 0.38196

2025
2025
2025
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IDS = Σᵢ [wᵢ × scoreᵢ / A_max] × κ_R
κ_R = 0.382 · U_R = 38.2 · A_max = 100
0 25 50 75 U_R 82.1 Google 78.5 OpenAI 71.2 Anthropic 69.8 Meta AI IDS Score (0–100) · κ_R = 0.382 · 2025

[1] CSR (2025). Theory C v4: Formal Derivation of the Rouss Constant. SINCROTROPIE Complex Systems. Primary derivation via κ_R = 1−√κ_R; Φ emerges as algebraic consequence.
[2] CSR (2025). Acta Constitutiva del SINCSys Framework v5. Apéndice G: Glosario de Constantes y Fórmulas. Definición actualizada de κ_R con derivación de auto-referencia.
[3] Planck Collaboration (2018). Planck 2018 results. VI. Cosmological parameters. A&A 641, A6. ΩΛ = 0.6847, Ωc h² = 0.1200. Ratio ΩΛ/Ωc ≈ 2.626 vs. Φ² = 2.6180 (< 0.3% error).
[4] IDS benchmark scores are computed from public documentation, deployment footprints, and stated alignment policies as of Q3 2025. Individual scores are the author's measurement under the SINCSys standard, not official figures from the rated organizations.

κ_R = 1 − √κ_R = 1/Φ² ≈ 0.382
U_R = κ_R × A_max = 38.2
IDS = Σᵢ [wᵢ × scoreᵢ / A_max] × κ_R

Google DeepMind
82.1
OpenAI
78.5
Anthropic
71.2
Meta AI
69.8

κ_R = 1 − √κ_R = 1/Φ² ≈ 0.382
U_R = κ_R × A_max = 38.2
D* = H / κ_R = H · Φ²
IDS = Σᵢ [wᵢ × scoreᵢ / A_max] × κ_R
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Theory C v4 · CSR · 2025