E_nuclear
Nuclear energy scale in Recognition Science equals the coherence energy multiplied by phi to the 45th power. Engineers and physicists comparing storage densities across chemical and nuclear regimes cite this definition to anchor the upper rung of the phi-ladder. The declaration is a direct composition of the phi-rung energy function with the fixed nuclear rung index.
claimThe nuclear energy scale is defined by $E_mathrm{nuclear} = E_mathrm{coh} cdot phi^{45}$, where $E_mathrm{coh}$ is the coherence energy per recognition event and $phi$ is the golden ratio.
background
The EN-004 module derives energy storage limits from the Recognition Science J-cost structure, where energy equals J-cost times the coherence quantum $E_mathrm{coh} = phi^{-5}$ eV. The phi-rung energy function maps each integer rung $n$ to $E_mathrm{coh} cdot phi^n$, with the nuclear rung fixed at 45 to reproduce the observed nuclear-to-chemical ratio near $10^9$. Upstream, nuclear_rung supplies the constant index 45 while phi_rung_energy supplies the scaling law.
proof idea
This is a one-line definition that applies the phi_rung_energy function to the nuclear_rung constant.
why it matters in Recognition Science
The definition supplies the nuclear energy value required by the nuclear_exceeds_chemical theorem and the rs_energy_storage_hierarchy theorem. It completes the nuclear limit inside the EN-004 hierarchy, placing chemical energy at rung 0 and nuclear energy at rung 45 to produce the factor $phi^{45}$. The construction aligns with the phi-ladder and the eight-tick octave periodicity of the Recognition Science forcing chain.
scope and limits
- Does not derive the rung index 45 from the J-cost equation.
- Does not incorporate mass-energy equivalence $mc^2$.
- Does not address volume or mass density conversion factors.
- Does not vary with specific nuclear species or isotopes.
formal statement (Lean)
90def E_nuclear : ℝ := phi_rung_energy nuclear_rung
proof body
Definition body.
91
92/-- **THEOREM EN-004.4**: Nuclear energy exceeds chemical energy. -/