E_nuclear
plain-language theorem explainer
Nuclear energy scale is defined as coherence energy multiplied by phi to the 45th power on the recognition ladder. Modelers of energy hierarchies in Recognition Science cite this to set the nuclear rung that produces the observed 10^9 ratio to chemical scales. The definition is a direct composition of the rung-energy function with the fixed nuclear index.
Claim. $E_ {nuclear} := E_{coh} · φ^{45}$, where $E_{coh}$ is the coherence storage energy and φ is the golden-ratio fixed point of the J-cost equation.
background
The Energy Storage Density Structure module builds energy scales from the φ-ladder. phi_rung_energy(n) returns E_coh_storage multiplied by φ^n, the stored energy per recognition event at rung n. nuclear_rung is the constant integer 45 chosen to reproduce the nuclear-to-chemical ratio of order 10^9.
proof idea
One-line definition that applies phi_rung_energy to nuclear_rung.
why it matters
This supplies the nuclear scale used by nuclear_exceeds_chemical and rs_energy_storage_hierarchy. It fills the EN-004 step that places nuclear energy at rung 45 on the φ-ladder, confirming the hierarchy chemical < nuclear < mass-energy with successive factors of φ^45. The module doc states the prediction E_nuc / E_chem = φ^45 ≈ 10^9.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.