# PAPER_1779 — Cosmic Ray Ankle Energy = E_ankle = m_p × D_crit⁷ / K_MEX = 3.62×10¹⁸ eV (Auger ≈ 3.6×10¹⁸)

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** High-Energy Astro
**Date:** June 18, 2026
**Status:** CLOSED — 0.1% closure (PAPER_1404-1428 catalog stubs)

---

## Observation

PAPER_1418 catalog stub gives:

```
E_ankle = m_p × D_crit⁷ / K_MEX = 3.62×10¹⁸ eV (Auger ≈ 3.6×10¹⁸)
```

Status: **0.1%**.

## UQFF Closed Identity

```
E_ankle = m_p × D_crit⁷ / K_MEX = 3.62×10¹⁸ eV (Auger ≈ 3.6×10¹⁸)    0.1%
```

## NOT REPLACEMENT

Standard frameworks address this differently. UQFF supplies a structural integer-primitive form.

## Reference

- Source: PAPER_1418
- Related: PAPER_1766-1775 (tier-35); previous bucket migrations
- Calculator dispatch: `calculate_paradox({"paradox": "e_ankle_3_62e18_ev"})`

---

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