Constants Hartree Rydberg Score Card Row Bohr Over Reduced Compton Bracket

A dimensionless radius ratio

The Bohr radius is the characteristic size of a hydrogen atom in the Bohr model, roughly 5.29 × 10⁻¹¹ meters. The reduced Compton wavelength is a quantum scale associated with the electron, about 3.86 × 10⁻¹³ meters. Their ratio, about 137, is not a coincidence of units; it is the inverse fine-structure constant, a dimensionless number that sets the strength of electromagnetic interactions.

The declaration row_bohr_over_reduced_compton_bracket states, as a theorem in the framework's machine-checked library of formal theorems, that this ratio lies strictly between 137.030 and 137.039. This is not a measurement; it is a certified interval bound derived from the framework's own inverse fine-structure constant, which is itself a defined quantity. The theorem confirms that the dimensionless ratio is consistent with the known value of the inverse fine-structure constant, approximately 137.036.

In Recognition Science, the framework models physical constants as ratios that emerge from a forcing chain, not as free parameters. Here, the ratio of the Bohr radius to the reduced Compton wavelength is defined to equal the framework's inverse fine-structure constant. The theorem's bracket is a tight window: it says the ratio is greater than 137.030 and less than 137.039, with no other numerical content.

The declaration does not claim a value in joules or meters. It records only the dimensionless ratio and its bounds. Converting to SI units would require an electron mass, Planck's constant, the speed of light, and a display bridge that maps the dimensionless ratio to measured Hartree, Rydberg, or Bohr-radius values. That bridge is not part of this theorem.

The practical consequence is a clean, unit-free check: the framework's inverse fine-structure constant reproduces the classical hydrogen scale ratio within a narrow band. The falsifier is explicit: if CODATA's inverse fine-structure constant fell outside (137.030, 137.039), or if an SI bridge failed to map the ratio to measurements, the theorem's premise would fail.

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⟩

/-- P1-C03 dimensionless Bohr/reduced-Compton radius ratio. -/
noncomputable def row_bohr_over_reduced_compton : ℝ := alphaInv

/-- P1-C03 dimensionless Bohr/reduced-Compton radius ratio. -/
noncomputable def row_bohr_over_reduced_compton : ℝ := alphaInv

What this page does not claim

The declaration does not claim a Joule or meter value for the Hartree, Rydberg, or Bohr-radius constants. The declaration does not claim that the inverse fine-structure constant is derived from first principles within this module; it is a defined quantity. The declaration does not claim the framework's inverse fine-structure constant is exactly equal to the CODATA measured value; it only certifies a narrow interval.

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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