Rydberg constant R_∞

The Rydberg constant R_∞ is, in the τ-framework, a Layer-4 verification readout of the cascade — derived as R_∞ = α² m_e c / (2h) from the τ-predicted α and m_e. It inherits the 0.025 ppm precision of the mass-ratio chain (Tier A) and is one of five constants the τ-cascade predicts to better than 1 ppm.

Categorical invariant. R_∞ = α² m_e c / (2h) — the hydrogen-spectrum readout that closes the verification layer.

Primary registry anchor: IV.D199

Supporting items: IV.T218, IV.D407, IV.D255, V.T157

1. I.K0 — Universe Postulate
2. IV.D255 — Master constant ι_τ
3. IV.D407 — α = (11/15)² ι_τ⁴
4. IV.T218 — Electron Mass — m_e = m_n / R
5. IV.D199 — Rydberg constant — R_∞ = α² m_e c / (2h)
6. V.T157 — Calibration Sufficiency — R_∞ is a Layer-4 verification readout

Lean modules referenced: TauLib.BookIV.Calibration.SIReference, TauLib.BookV.Coda.ConstantsLedger

Numerical value: 10973731.568160 ± 0.000021 m⁻¹

Calibration anchor: PG-P01-neutron

Calibration chain:

1. Layer 0: ι_τ = 2/(π + e_math)
2. Layer 1: α = (11/15)² ι_τ⁴
3. Layer 2: m_e = m_n / R
4. Layer 4: R_∞ = α² m_e c / (2h) = 1.097 373 157 × 10⁷ m⁻¹
5. τ-predicted vs CODATA: 0.025 ppm (Tier A — flagship precision)

Manuscript reference: manuscript-sources/book-04/part06/ch45-hydrogen-atom-bohr-rydberg.tex

Status: Formalized

Module: TauLib.BookIV.Calibration.SIReference

Lean kind: def

Related glossary entries

• PG-C02-iota-tau Master constant ι_τ
• PG-C05-fine-structure-alpha Fine-structure constant α
• PG-C09-electron-mass Electron mass m_e
• PG-P01-neutron τ-Neutron

Referenced by

• PG-C12-bohr-radius Bohr radius a_0