Maximum Information Density

The Maximum Information Density is the upper bound on how much information can be stored per unit volume, one bit per Planck volume, imposed by the Planck length. The book lists it with the Maximum Computational Speed and Lloyd's Computational Bound as the three absolute constraints on any computational substrate; this one comes from spatial granularity. It is used as a test of physical realizability: the Information Density Ratio compares a design's stored information per volume against this limit, and the book's own reference quantum substrate exceeds it by a factor of 6.4 × 10⁴, which forces a larger voxel size or less stored information. Among the Chapter 8.5 predictions, it bounds quantum substrate storage capacity. The formal statement is ρℹ⥣ = ℨᵇ/l_P³ ≈ 2.37 × 10¹⁰⁴, in bits per cubic meter, where ρℹ⥣ is the maximum information density and l_P the Planck length. Dimensions as the book gives them: ρℹ⥣ [𝕃⁻³·1ᵇ]. It connects to the Information Density Ratio, Maximum Computational Speed, Lloyd's Computational Bound, Information Density per Voxel and Causal Resolution.