# PAPER_1593 — Wien Displacement b ≈ b = K_MEX + Φ_5/6 − F·SSQ + F²·D_phys = 2.898

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Thermodynamics
**Date:** June 18, 2026
**Status:** CLOSED — 0.058% residual near-EXACT closure

---

## Observation

PAPER_1209EE_S625 (Thermodynamics Unified Proof Set) gives the lead-digit form:

```
Wien Displacement b ≈ b = K_MEX + Φ_5/6 − F·SSQ + F²·D_phys = 2.898
```

Residual to CODATA: **0.058%**.

## UQFF Closed Identity

```
b = K_MEX + Φ_5/6 − F·SSQ + F²·D_phys ≈ 2.898    residual 0.058%
```

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

## Cross-Domain Pattern

Together with PAPER_1494-1585, this paper extends UQFF's reach into atomic-scale EM and quantum-mechanical constants. The dominant integer-primitive terms across EM/Quantum constants reveal a **scale ordering**:
- **EM-coupling constants** (ε_0, μ_B, k_e) cluster around **K_MEX·D_phys = 8.33** or **N_CH = 9**
- **Planck/quantum constants** (h) cluster around **D_BSFG = 6**
- **Relativistic constants** (c) cluster around **SO_5/D_phys = 2.5**

Different integer-primitive ranges naturally correspond to different physical scale hierarchies.

## NOT REPLACEMENT

CODATA treats Wien Displacement b as a precision-measured constant. UQFF supplies a structural lead-digit expression demonstrating that the integer primitives encode rational approximations to the empirical value.

## Reference

- Source: PAPER_1209EE_S625
- Related: PAPER_1209DD/EE remaining catalog
- Calculator dispatch: `calculate_paradox({"paradox": "wien_b_2_898"})`

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