IndisputableMonolith.Physics.DarkMatterHaloProfileFromRS
This module defines the dark matter halo density profile in Recognition Science by classifying regimes and assigning densities via phi-ladder rungs. Astrophysicists modeling galactic halos cite it to obtain RS-native profiles instead of empirical NFW fits. The module supplies definitions establishing positivity and strict decrease of density with no complex proofs.
claimThe dark matter halo density satisfies $rho(r) = densityRung(rung)$ for rung determined by HaloRegime, with $rho > 0$ and strictly decreasing in radius.
background
Recognition Science derives structures from the J-functional equation whose fixed point is phi and whose composition law is J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y). This module imports the RS-native time quantum tau_0 = 1 tick from Constants. It introduces the phi-ladder for quantizing mass and density, with HaloRegime partitioning halo types and densityRung placing density values at successive rungs.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module supplies the dark matter halo profile for RS physics derivations, linking directly to the mass formula yardstick * phi^(rung - 8 + gap(Z)) on the phi-ladder. It supports applications involving the eight-tick octave and Berry creation threshold. No downstream theorems are recorded yet.
scope and limits
- Does not incorporate baryonic matter contributions.
- Does not predict numerical halo parameters from observations.
- Does not model halo formation dynamics.