IndisputableMonolith.Gravity.RunningGDerivation
This module defines the voxel density scaling N(r) that supports derivations of scale-dependent gravity in Recognition Science. Physicists examining running constants at nanometer scales would cite it. The module supplies definitions and scaling relations built directly on the imported Constants, Cost, and RunningG modules.
claimThe effective number of recognition voxels is given by the function $N(r)$ of radius $r$.
background
The module belongs to the Gravity domain. It imports Constants (setting the RS time quantum τ₀ = 1 tick), Cost (for recognition cost functions), and RunningG (which states that G(r) → G_∞ as r → ∞ while running at small scales). The central definition is the voxel density scaling that gives the effective number of recognition voxels N(r).
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module supplies the voxel density scaling that underpins the gravitational running formalized in the RunningG module (C51). It connects cost-based recognition to observable modifications of G at small radii.
scope and limits
- Does not derive an explicit closed-form expression for N(r).
- Does not compute numerical values of N(r) at chosen radii.
- Does not link the scaling to the phi-ladder mass formula.