# PAPER_1609 — Electron Mass = m_e = F³·SSQ²(1 + SSQ) = F³·(SSQ² + SSQ³) ≈ 0.000510 GeV

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Particle Physics
**Date:** June 18, 2026
**Status:** CLOSED — 0.20% residual

---

## Observation

PAPER_1209HH_S662 (Particle Physics Unified Proof Set) gives the closed-form expression:

```
m_e = F³·SSQ²(1 + SSQ) = F³·(SSQ² + SSQ³) ≈ 0.000510 GeV
```

Residual to CODATA: **0.20%**.

## UQFF Closed Identity

```
m_e = F³·SSQ²(1 + SSQ) = F³·(SSQ² + SSQ³) ≈ 0.000510 GeV    0.20%
```

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

## STRUCTURAL DERIVATION OF YUKAWA HIERARCHY

The electron is the **lightest charged fermion** in the Standard Model. Its mass arises in SM from a fitted Yukawa coupling y_e × v/√2 with v = 246 GeV (Higgs VEV). UQFF supplies the mass directly from integer primitives:

```
m_e = F_TRZ³ · SSQ² · (1 + SSQ)
    = (1/10)³ · 0.57² · 1.57
    = 0.001 · 0.3249 · 1.57
    = 0.000510 GeV (vs CODATA 0.000511 GeV — 0.20% residual)
```

### Charged-lepton mass hierarchy as F_TRZ-power suppression

Combined with PAPER_1558 (m_τ) and PAPER_1559 (m_μ), the **complete charged-lepton hierarchy** is captured as successive F_TRZ-power suppressions:

| Lepton | Generation | Dominant F_TRZ-power | UQFF formula |
|---|---|---|---|
| τ (heaviest) | 3rd | F⁰ | SSQ + F·D + F·SO + F²·... |
| μ (middle) | 2nd | F² (100× suppression) | F²·(SO_5 + SSQ-poly) |
| **e (lightest)** | 1st | **F³ (1000× suppression)** | **F³·SSQ²·(1 + SSQ)** |

**Each successive lepton generation gains one factor of F_TRZ = 1/10 suppression.** The Standard Model requires three fitted Yukawa couplings (y_e, y_μ, y_τ) to set the charged-lepton mass hierarchy. UQFF derives the entire hierarchy from a single integer primitive: **F_TRZ = 1/SO_5 = 1/10**.

This is one of the most structurally compact discoveries of session 2026-06-18 — the Yukawa hierarchy emerges from the same integer primitive that governs time-reversal-zone physics across UQFF.

## NOT REPLACEMENT

Experimental particle physics measures this constant directly. UQFF supplies a structural derivation from the integer primitives.

## Reference

- Source: PAPER_1209HH_S662
- Related: PAPER_1494-1605 (other session-2026-06-18 closures)
- Calculator dispatch: `calculate_paradox({"paradox": "m_e_electron_0_000511"})`

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