Hartree and Rydberg Inside CODATA Brackets

1. Setting

Hartree and Rydberg Inside CODATA Brackets is anchored in Constants.HartreeRydbergScoreCard. The page is not a loose explainer: it is a public map from the Recognition Science forcing chain into one Lean-checked declaration bundle. The primary anchor determines what is proved, and the surrounding declarations show how the result is used.

2. Equations

(E1)

$$ J(x)=\frac12(x+x^{-1})-1,\qquad \varphi^2=\varphi+1 $$

Shared constant-forcing backbone.

3. Prediction or structural target

• Structural target: Constants.HartreeRydbergScoreCard must keep resolving in the Lean canon, and all downstream pages that cite this anchor must continue to type-check.

This page is currently a structural derivation. Where the claim has direct empirical content, the prediction table gives the measurable target; otherwise the claim is a formal bridge inside the Lean canon.

4. Formal anchor

The primary anchor is Constants.HartreeRydbergScoreCard..row_hartree_over_rest_bracket.

theorem row_hartree_over_rest_bracket :
    (5.32e-5 : ℝ) < row_hartree_over_rest ∧
      row_hartree_over_rest < (5.33e-5 : ℝ) :=
  ⟨row_hartree_over_rest_lower, row_hartree_over_rest_upper⟩

theorem row_rydberg_over_rest_lower :
    (2.66e-5 : ℝ) < row_rydberg_over_rest := by
  rw [row_rydberg_over_rest_eq]
  have hsqpos : 0 < alphaInv ^ 2 := sq_pos_of_ne_zero (ne_of_gt alphaInv_pos)

5. What is inside the Lean module

Key theorems:

• alphaInv_pos
• row_hartree_over_rest_eq
• row_rydberg_over_rest_eq
• row_hartree_over_rest_lower
• row_hartree_over_rest_upper
• row_hartree_over_rest_bracket
• row_rydberg_over_rest_lower
• row_rydberg_over_rest_upper
• row_rydberg_over_rest_bracket
• row_bohr_over_reduced_compton_eq
• row_bohr_over_reduced_compton_bracket
• hartreeRydbergScoreCardCert_holds

Key definitions:

• row_hartree_over_rest
• row_rydberg_over_rest
• row_bohr_over_reduced_compton
• HartreeRydbergScoreCardCert

6. Derivation chain

• row_hartree_over_rest_bracket - Hartree bracket
• row_rydberg_over_rest_bracket - Rydberg bracket
• row_bohr_over_reduced_compton_bracket - Bohr / Compton bracket
• hartreeRydbergScoreCardCert_holds - Score card holds

7. Falsifier

An atomic-spectroscopy measurement that places any of these dimensionless ratios outside the certified bracket refutes the score card.

8. Where this derivation stops

Below this page the chain reduces to the RS forcing sequence: J-cost uniqueness, phi forcing, the eight-tick cycle, and the D=3 recognition substrate. If any upstream theorem changes, this page must be versioned rather than patched silently. The published URL is stable, but the version field is the contract.

11. Why this belongs in the derivations corpus

The corpus is organized around load-bearing consequences, not around file names. This entry is included because Constants.HartreeRydbergScoreCard contributes a reusable theorem or definitional bridge that other pages can cite. Keeping the page public gives readers a stable URL, a JSON record, and a direct path into the Lean theorem page. If the entry becomes redundant with a stronger derivation later, the current slug should be retired rather than silently rewritten; the replacement should absorb its anchors and preserve the audit history.