nuclear_chemical_ratio
plain-language theorem explainer
Recognition Science sets the nuclear-to-chemical energy ratio exactly to φ^45. Engineers comparing storage scales on the φ-ladder cite this constant when establishing the hierarchy chemical < nuclear. The declaration is a direct definition that supplies the value used in the immediate successor inequality.
Claim. The nuclear-to-chemical energy ratio is defined by $E_ {nuc}/E_{chem} = φ^{45}$.
background
In the EN-004 module on Optimal Energy Storage Density, energy takes the form E = J(x) · E_coh where E_coh = φ^{-5} eV and J(x) = ½(x + x^{-1}) - 1. Chemical storage is capped at one coherence quantum per bond while nuclear storage advances along the φ-ladder by roughly 45 rungs. The module states that this produces the ratio φ^45 ≈ 10^9 and places nuclear storage between chemical and mass-energy limits.
proof idea
This declaration is a direct definition that assigns phi raised to the 45th power to the ratio symbol.
why it matters
The definition supplies the exact ratio required by the downstream theorem nuclear_chemical_ratio_gt_one, which proves the ratio exceeds unity. It realizes the module claim that E_nuc/E_chem = φ^45 matches known nuclear/chemical scales and anchors the energy-storage hierarchy inside the Recognition framework. The result sits inside the φ-ladder structure that follows from the forced self-similar fixed point.
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