neutronStarCert
plain-language theorem explainer
The certificate neutronStarCert asserts that neutron-star crusts comprise five regimes with successive densities in exact golden-ratio proportion and everywhere positive. Astrophysicists working within Recognition Science would cite it to confirm that the phi-ladder reproduces the canonical five-layer structure. It is assembled by a direct record constructor that inserts the regime cardinality, the density-ratio identity, and the positivity theorem.
Claim. Let $NeutronStarCert$ be the structure asserting that the neutron-star crustal regimes number exactly five, that the ratio of densities on adjacent rungs equals the golden ratio $phi$, and that every density is positive. The definition supplies this certificate by setting the regime count to the cardinality of the regime enumeration, the ratio to the established density-ratio identity, and positivity to the density-positivity theorem.
background
Recognition Science models neutron-star crusts via the phi-ladder of densities. The module enumerates five regimes (outer crust, inner crust, nuclear pasta, outer core, inner core) and defines density at rung k as proportional to $phi^k$ (MODULE_DOC). NeutronStarCert packages the three properties: exact count of five, adjacent ratio exactly $phi$, and strict positivity. Upstream density_ratio and density_pos theorems establish the ratio and positivity by unfolding the power definition and applying ring arithmetic; identical lemmas appear in battery chemistry and dark-matter halo profiles.
proof idea
The definition is a one-line record constructor. It populates the five_regimes field from nsRegime_count, the phi_ratio field from density_ratio, and the density_always_pos field from density_pos.
why it matters
This supplies the concrete instance of NeutronStarCert that certifies the neutron-star crust as a realization of the Recognition Science phi-ladder. It draws on the density lemmas proved earlier in the module and on the generic phi_ratio from the quasicrystal development. The construction links the abstract forcing chain (T6 self-similar fixed point) to a specific astrophysical density profile whose regime count is five; no downstream theorems yet depend on it.
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