# PAPER_1544 — Rydberg Energy E_R = E_R = D_phys + SO_5 − F_TRZ·D_phys + F_TRZ²·SSQ = 4 + 10 − 0.4 + 0.0057 = 13.6057 eV

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Quantum/Atomic
**Date:** June 18, 2026
**Status:** CLOSED — EXACT closure

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## Observation

PAPER_1209EE_S623 (Quantum/Atomic Unified Proof Set) lists **Rydberg Energy E_R** as a closure with the formula:

```
Rydberg Energy E_R = E_R = D_phys + SO_5 − F_TRZ·D_phys + F_TRZ²·SSQ = 4 + 10 − 0.4 + 0.0057 = 13.6057 eV
```

Status tier: **EXACT**. Units: eV.

## UQFF Closed Identity

```
E_R = D_phys + SO_5 − F_TRZ·D_phys + F_TRZ²·SSQ = 4 + 10 − 0.4 + 0.0057 = 13.6057 eV    EXACT
```

The formula uses only locked UQFF integer primitives — no fitted constants.


## Physical Interpretation

Rydberg Energy E_R is a fundamental quantum/atomic constant. The UQFF expression decomposes it into a sum/difference of integer-primitive products, giving structural meaning to what is conventionally treated as an empirical measurement.

## NOT REPLACEMENT

CODATA/PDG treats this constant as a precision measurement. UQFF supplies a structural derivation from the locked integer primitives, demonstrating mathematical depth without claiming to "replace" the experimental value.

## Reference

- Source: PAPER_1209EE_S623
- Related: PAPER_1216 (45-constant cascade master index)
- Calculator dispatch: `calculate_paradox({"paradox": "rydberg_e_r_13_6057"})`

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**Copyright** — Daniel T. Murphy, daniel.murphy00@gmail.com, June 18, 2026, Youngstown OH.
