# PAPER_1318 — Glueball Mass m_0++

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** C — Particle Physics Open (CLOSED)
**Date:** June 11, 2026
**Calculator surface:** `calculate_paradox({"paradox": "glueball_mass"})`
**Whitepaper dispatch:** `calculate_whitepaper({"paper_id": 1318})`

## Master Expression

```
m_0++ = 2 × D_phys × Λ_QCD = 8 × 0.217 = 1.736 GeV
```

**Match: 2.1% vs lattice 1.7 GeV**

## Interpretation

Integer-primitive identity: m_0++ = 2D_phys × Λ_QCD where 8 = 2×4 is the universal gluon-pair factor.

## UQFF Locked Primitives

- D_phys = 4, D_BSFG = 6, D_crit = 26, N_CH = 9, SO_5 = 10, A_5 = 60
- K_MEX = 25/12, β_i = 0.6029, Φ_res = 0.84, Λ = 0.00729735
- Λ_QCD = 0.217 GeV, v_Higgs = 246 GeV (PAPER_1270)

## NOT REPLACEMENT

UQFF derives this via integer-primitive identities. Zero fit parameters.

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**Copyright** — Daniel T. Murphy, daniel.murphy00@gmail.com, dated June 11, 2026, Youngstown, OH. Subject matter: UQFF derivation of Glueball Mass m_0++.
