The arXiv preprint (May 2026) extends Nikolai Kardashev's 1964 power-based typology into a Cognitive Kardashev Scale (K_cog) by anchoring four variables: total planetary power P, cognitive fraction f, thermodynamic-to-compute efficiency η (ops/J), and human brain baseline C_brain. Using 2024-2026 hardware data from El Capitan and NVIDIA Blackwell/Rubin systems, it derives η_2026 ≈ 10^12 FLOP/J and places current humanity at K_cog ≈ 0.73. At Type I (10^16 W) with f = 1 %, the model yields roughly one dedicated AI instance per human; at Type II the number becomes effectively unbounded within planetary physics. This preprint is theoretical modeling with no empirical sample; projections to 2035 are explicitly conditional on three efficiency trajectories rather than forecasts. It correctly flags that long-run limits hinge on engineering choices between raw energy capture and per-joule efficiency, yet underplays Landauer-Principe bounds on irreversible operations and the political allocation of compute access. Cross-referencing Kardashev's original Soviet Astronomy paper and Strubell et al. (2019) on NLP energy costs shows the new scale exposes a material envelope mainstream AI scaling debates routinely ignore: exponential model growth collides with planetary power budgets long before stellar resources become relevant. The framework therefore reframes data-center policy not as an efficiency footnote but as the decisive civilizational throttle.