The Paula Scale: Measuring Progress Toward Simulable Completeness

This paper proposes the Paula Scale, a formal metric for measuring progress in quantum simulation capacity — defined as the scale of physical reality that a computing infrastructure can faithfully simulate at the quantum level. Three discrete Q-Levels are defined, anchored in physical system sizes: molecular simulation (Q-Level One, ~10³ particles), planetary simulation (Q-Level Two, ~10⁵⁰ particles), and universal simulation (Q-Level Three, ~10⁸⁰ particles). Qubit requirements are derived quantities, not definitional thresholds. A piecewise logarithmic interpolation formula places Earth at Q-Level 0.25–0.33 as of early 2026. The paper situates the Paula Scale relative to Kardashev (energy), Sagan (information), Barrow (manipulation), and Lloyd (computational bounds), arguing that simulation capacity occupies a distinct and previously unoccupied axis. A maturity qualifier (α/β/γ) addresses circuit depth as a complementary dimension. The Paula Scale measures not how much energy a civilisation uses nor how small a scale it can engineer, but how deeply it can understand the physical world through computation.