# PAPER_1314 — Fermion Mass Spectrum Hierarchy m_e to m_t

**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": "mass_hierarchy_full"})`
**Whitepaper dispatch:** `calculate_whitepaper({"paper_id": 1314})`

## Master Expression

```
m_t/m_e ≈ 3.4×10⁵; UQFF geometric bound via integer lattice
```

**Match: STRUCTURAL bound**

## Interpretation

Hierarchy dissolves — no fundamental Planck scale. Masses are geometric projections from integer lattice.

## 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 Fermion Mass Spectrum Hierarchy m_e to m_t.
