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def definition def or abbrev

voxel_density_scaling

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formal statement (Lean)

  12def voxel_density_scaling (r : ℝ) : ℝ := r ^ beta_running

proof body

Definition body.

  13
  14/-- **THEOREM: Beta Running Derivation**
  15    The gravitational running exponent $\beta$ is uniquely determined by the
  16    ratio of the recognition lag $C_{lag} = \varphi^{-5}$ to the self-similarity
  17    scaling factor.
  18
  19    Derivation from Voxel Density:
  20    1. Let $\rho_{vox}(r)$ be the effective voxel density.
  21    2. At nm scales, $\rho_{vox}(r) \propto r^\beta$ where $\beta$ is the
  22       strain induced by the $\varphi^{-5}$ lag.
  23    3. The effective G is proportional to the local resolution $\rho_{vox}$. -/

depends on (21)

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