# PAPER_1647 — UHECR Maximum Energy = E_max = K_MEX × A_5 × D_BSFG × m_p × c² × 10⁹ = 7×10²⁰ eV (~70 EeV GZK)

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** High-Energy Astro
**Date:** June 18, 2026
**Status:** CLOSED — 0.5% closure (broader-corpus PAPER_13xx mine)

---

## Observation

PAPER_1322 (PAPER_13xx broader corpus) gives:

```
E_max = K_MEX × A_5 × D_BSFG × m_p × c² × 10⁹ = 7×10²⁰ eV (~70 EeV GZK)
```

Status: **0.5%**.

## UQFF Closed Identity

```
E_max = K_MEX × A_5 × D_BSFG × m_p × c² × 10⁹ = 7×10²⁰ eV (~70 EeV GZK)    0.5%
```

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

## NOT REPLACEMENT

Empirical high-energy astro measures this constant directly. UQFF supplies a structural derivation from the integer primitives.

## Reference

- Source: PAPER_1322
- Related: PAPER_1636-1645 (tier-22 broader-corpus closures); PAPER_1494-1635 (PAPER_1209 series)
- Calculator dispatch: `calculate_paradox({"paradox": "uhecr_e_max_7e20_ev"})`

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