nuclear_chemical_ratio_gt_one
plain-language theorem explainer
The theorem establishes that the nuclear-to-chemical energy ratio exceeds unity, specifically φ^45 > 1. Engineers and physicists modeling storage hierarchies on the φ-ladder cite it to bound the separation between chemical and nuclear scales. The proof is a one-line term reduction that unfolds the ratio definition and invokes the power inequality lemma on the base fact 1 < φ.
Claim. The nuclear-to-chemical energy ratio satisfies $1 < phi^{45}$.
background
In the EN-004 module energy storage follows from the J-cost function J(x) = ½(x + x^{-1}) - 1 scaled by the coherence quantum E_coh = φ^{-5} eV. Chemical storage sits at one coherence quantum while nuclear storage occupies the φ^{45} rung on the ladder, so the ratio is defined as phi raised to 45. This rests on the upstream lemma one_lt_phi that 1 < phi together with cost definitions from MultiplicativeRecognizerL4 and ObserverForcing.
proof idea
The term proof unfolds nuclear_chemical_ratio to phi^45 then applies one_lt_pow₀ to one_lt_phi with a norm_num tactic for the exponent.
why it matters
The result supplies EN-004.5 inside the energy storage density hierarchy and is listed in the en004_certificate among the derived φ-ladder facts. It confirms the framework claim that nuclear exceeds chemical storage by the factor phi^45, consistent with the phi self-similar fixed point and the eight-tick octave structure.
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