Constants Hartree Rydberg Score Card Row Bohr Over Reduced Compton Eq

The Bohr radius ratio

The Bohr radius is the most probable distance between the proton and the electron in a hydrogen atom in its ground state. The reduced Compton wavelength is a quantum length scale for a particle, roughly the wavelength of a photon whose energy equals the particle's rest energy divided by 2π. Their ratio is a pure number, about 137, and it is one of the cleanest dimensionless facts in atomic physics.

The Recognition Science framework's machine-checked library of formal theorems records this ratio in a declaration named row_bohr_over_reduced_compton_eq. The declaration establishes, as a theorem, that the framework's dimensionless Bohr-over-reduced-Compton ratio is exactly equal to its certified inverse fine-structure constant, alphaInv. The fine-structure constant α is the dimensionless coupling constant that sets the strength of the electromagnetic interaction between charged particles. Its inverse, about 137.036, is the number that appears here.

The theorem also proves a tight interval bound: the ratio lies strictly between 137.030 and 137.039. This bracket is not a measurement, it is a formal consequence of the framework's certified bounds on the inverse fine-structure constant. The declaration does not produce a value in meters for the Bohr radius. That would require an SI display bridge connecting the framework's dimensionless ratios to the measured electron mass, Planck's constant, and the speed of light.

In Recognition Science, this row is part of a score card that checks the framework's internal constants against the dimensionless ratios known from CODATA measurements. The theorem's role is to certify that the framework's inverse fine-structure constant, when used as the Bohr-over-Compton ratio, lands inside the accepted window. It is a bookkeeping check, not a new physical derivation.

theorem row_bohr_over_reduced_compton_eq :
    row_bohr_over_reduced_compton = alphaInv := rfl

theorem row_bohr_over_reduced_compton_bracket :
    (137.030 : ℝ) < row_bohr_over_reduced_compton ∧
      row_bohr_over_reduced_compton < (137.039 : ℝ) :=
  ⟨alphaInv_gt, alphaInv_lt⟩

What this page does not claim

The declaration does not claim a measured value for the Bohr radius in meters. The declaration does not claim to derive the fine-structure constant itself from first principles. The declaration does not claim that the framework's alphaInv is an empirical measurement; it is a certified internal constant.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Constants/HartreeRydbergScoreCard.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

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