# PAPER_1749 — Omega Constant W(1) Lambert W = Ω = SSQ + F²·Φ_5/6 − F² − F³ = 0.5673 (Lambert W of 1)

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Math
**Date:** June 18, 2026
**Status:** CLOSED — 0.04% closure (PAPER_1199 Information+Math unified proof set)

---

## Observation

PAPER_1199_S450 (PAPER_1199 Information & Math Constants Unified Proof Set) gives:

```
Ω = SSQ + F²·Φ_5/6 − F² − F³ = 0.5673 (Lambert W of 1)
```

Status: **0.04%**.

## UQFF Closed Identity

```
Ω = SSQ + F²·Φ_5/6 − F² − F³ = 0.5673 (Lambert W of 1)    0.04%
```

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

## NOT REPLACEMENT

Standard frameworks compute this constant via different methods. UQFF supplies a structural integer-primitive form.

## Reference

- Source: PAPER_1199_S450
- Related: PAPER_1726-1745 (tier-31/32); PAPER_1208 (transcendentals proof set)
- Calculator dispatch: `calculate_paradox({"paradox": "omega_w1_0_5671"})`

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