nuclear_rung
plain-language theorem explainer
Recognition Science assigns the nuclear binding energy to rung 45 on the phi-ladder. This integer constant produces the nuclear energy scale as the coherence quantum multiplied by phi to the 45th power, reproducing the observed 10^9 ratio to chemical energies. Engineers modeling storage density hierarchies cite the definition when applying the J-cost structure to bound practical limits. The declaration is a direct constant assignment with no lemmas or reduction steps.
Claim. The nuclear binding rung index is the integer $n=45$, which sets the exponent so that nuclear energy equals the coherence quantum times $phi^{45}$.
background
Recognition Science expresses stored energy as $E = J(x) · E_coh$ with $E_coh = phi^{-5}$ eV and $J(x) = ½(x + x^{-1}) - 1$. The phi-ladder organizes scales by integer rungs: chemical bonds sit at rung 0 while nuclear binding occupies a higher rung. The upstream scale definition supplies the power $phi^k$ for any natural number k. The module derives fundamental limits on energy storage density from this J-cost structure, predicting a strict hierarchy chemical < nuclear < mass-energy with each step differing by a factor near $10^9$.
proof idea
This is a direct definition that assigns the integer constant 45. No lemmas are invoked and no tactics are executed.
why it matters
The definition supplies the rung index required by the nuclear energy scale and by the theorem proving nuclear energy exceeds chemical energy. It fills the EN-004 claim on optimal energy storage density by fixing the nuclear rung at 45, consistent with the phi-ladder hierarchy. The parent results use this constant to establish the energy storage density hierarchy within the Recognition Science framework.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.