density
plain-language theorem explainer
Defines density at rung k on the Recognition Science phi-ladder as phi raised to the power k. Neutron-star crust modelers and nucleosynthesis calculations cite this to assign discrete densities across the five canonical regimes where adjacent layers scale by the golden ratio. The definition is a direct power assignment drawn from the constant phi.
Claim. For each natural number rung $k$, the density equals $phi^k$, where $phi$ is the self-similar fixed point satisfying the Recognition Composition Law.
background
The neutron star crustal regimes module organizes five regimes (outer crust through inner core) with densities placed on the phi-ladder. Adjacent regimes differ by the exact factor phi, as stated in the phi_ladder_step lemma: phi_ladder (n + 1) = phi * phi_ladder n. This definition supplies the explicit rung form used throughout the module.
proof idea
One-line definition that directly assigns phi raised to the power k.
why it matters
This definition supplies the density values consumed by nucleosynthesis tiers (of and phi_ladder_step) and by downstream calculations in ferromagnetism, metallic bonds, J-cost phase transitions, and cosmological constant modules. It implements the discrete phi-ladder rung step required by the neutron-star crustal regimes setup, consistent with the T5 J-uniqueness and T6 phi fixed-point landmarks.
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