coulombCoeff_consistent
Verification establishes that the Coulomb coefficient in nuclear binding energy calculations differs from its electromagnetic prediction by less than 0.2. Modelers applying the semi-empirical mass formula cite the bound to confirm parameter alignment between QCD inputs and observed nuclear scales. The proof is a one-line wrapper that unfolds the two coefficient definitions then applies numerical normalization.
claim$|C - C_p| < 0.2$, where $C$ denotes the Coulomb coefficient appearing in nuclear binding energy expressions and $C_p = (3/5) (1/137.036) (197.3 / 1.2)$ is the value predicted from electromagnetic considerations.
background
The module converts QCD-level inputs alpha_strong = 2/17 and string tension sigma = phi^{-5} into the coefficients of the semi-empirical mass formula. The predicted Coulomb coefficient is defined directly as (3/5) times the inverse fine-structure constant times a length-scale ratio. Upstream, r_min is the saturation radius given by sqrt(alpha_strong / stringTension), while the cellular-automata radius supplies a unit neighborhood size that remains peripheral to this numerical check.
proof idea
The proof is a one-line wrapper that unfolds the definitions of coulombCoeff and coulombCoeff_predicted, then applies norm_num to discharge the numerical inequality.
why it matters in Recognition Science
The result supplies a terminal consistency check inside the QCD-to-nuclear bridge, confirming that the electromagnetic term in binding energies stays within 0.2 of the value computed from the Recognition Science alpha band. It closes the numerical link between the string-tension and alpha_strong parameters and the semi-empirical mass formula without introducing further hypotheses.
scope and limits
- Does not derive the Coulomb coefficient from QCD dynamics alone.
- Does not extend the bound to nuclei far from saturation density.
- Does not incorporate higher-order electromagnetic or relativistic corrections.
- Does not remain valid under arbitrary changes to alpha_strong or string tension.
formal statement (Lean)
107theorem coulombCoeff_consistent : |coulombCoeff - coulombCoeff_predicted| < 0.2 := by
proof body
Term-mode proof.
108 unfold coulombCoeff coulombCoeff_predicted; norm_num
109
110/-! ## Saturation Properties -/
111
112/-- Nuclear saturation radius r_min = √(α_s/σ). -/