E_chemical
The definition sets the chemical energy scale to the base coherence quantum E_coh at rung zero on the phi-ladder. Engineers and physicists modeling RS-derived energy storage hierarchies cite it to anchor the chemical baseline before comparing to nuclear scales. It arises by direct substitution of the zero rung index into the general phi-rung energy expression.
claim$E_chemical = E_coh$ where $E_coh$ is the coherence quantum energy at rung zero of the phi-ladder.
background
Recognition Science places energy storage on the phi-ladder with energy at rung n given by E_coh times phi^n, where E_coh equals phi^{-5} eV. The module Engineering.EnergyStorageDensityStructure derives limits on energy density from this ladder and the J-cost structure, stating that energy equals J(x) times the coherence quantum. The chemical rung is fixed at index zero, representing one coherence quantum per bond. Upstream, phi_rung_energy supplies the general formula E_coh_storage * phi^n while chemical_rung supplies the index zero.
proof idea
The definition is a one-line wrapper that applies phi_rung_energy to the chemical_rung index of zero.
why it matters in Recognition Science
This supplies the base chemical scale referenced by rs_energy_storage_hierarchy and nuclear_exceeds_chemical, which establish the full hierarchy with nuclear energy exceeding chemical by phi^45. It realizes the EN-004 chemical limit of one coherence quantum per bond. In the framework it anchors the lowest rung of the phi-ladder, consistent with the J-uniqueness fixed point and the eight-tick octave.
scope and limits
- Does not convert the scale to electron-volt units.
- Does not incorporate variable J-cost factors beyond the rung index.
- Does not derive the nuclear rung index of 45.
Lean usage
example : E_chemical = E_coh_storage := by simp [E_chemical, phi_rung_energy, chemical_rung]formal statement (Lean)
87def E_chemical : ℝ := phi_rung_energy chemical_rung
proof body
Definition body.
88
89/-- Nuclear energy scale = E_coh · φ^45. -/