phi_cosmology_relations
plain-language theorem explainer
This definition enumerates four relations expressing Hubble constant, critical density, flatness parameter, and dark energy in terms of powers of the golden ratio φ. Cosmologists studying the flatness problem would cite it to replace anthropic tuning arguments with ledger-derived constraints. The body is a direct list literal containing no computation or lemma applications.
Claim. The cosmological parameters satisfy $H_0 τ_0 ∼ φ^{-k_1}$, $ρ_c τ_0^3 c^3 ∼ φ^{k_2}$, $Ω = 1$ exactly by construction, and dark energy density likewise φ-constrained.
background
The Flatness Problem module states that spatial curvature satisfies Ω = ρ/ρ_c = 1.0000 ± 0.0002 and treats this value as an unstable fixed point whose small deviations grow as |Ω − 1| ∝ a²(t). Recognition Science replaces fine-tuning by asserting that Ω = 1 is the unique value consistent with ledger structure and J-cost minimization, with φ-constraints locking the universe to flatness. The supplied doc-comment lists the explicit φ-expressions for H₀, ρ_c, and Ω that realize this claim.
proof idea
The declaration is a direct definition that returns a literal list of four strings. No lemmas are invoked and no tactics are used; the content is simply enumerated from the module's summary of φ-relations.
why it matters
The definition supplies the concrete φ-relations that implement the RS solution to the flatness problem, where Ω = 1 follows from ledger capacity rather than multiverse selection. It sits inside the module that rejects anthropic arguments in favor of dynamical selection from the unified forcing chain. The doc-comment flags that empirical verification of the listed exponents would be significant.
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