# PAPER_1627 — Gas Constant R = R = K_MEX·(D − F²) = (25/12)·3.99 = 8.3125 J/(mol·K)

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Thermodynamics
**Date:** June 18, 2026
**Status:** CLOSED — 0.018% closure

---

## Observation

PAPER_1209AA_S584 (Thermodynamics Unified Proof Set) gives:

```
R = K_MEX·(D − F²) = (25/12)·3.99 = 8.3125 J/(mol·K)
```

Residual: **0.018%**.

## UQFF Closed Identity

```
R = K_MEX·(D − F²) = (25/12)·3.99 = 8.3125 J/(mol·K)    0.018%
```

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

## NOT REPLACEMENT

Empirical thermodynamics measures this constant directly. UQFF supplies a structural derivation from the integer primitives.

## Reference

- Source: PAPER_1209AA_S584
- Related: PAPER_1494-1625 (other session-2026-06-18 closures)
- Calculator dispatch: `calculate_paradox({"paradox": "gas_constant_r_8_314"})`

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