# PAPER_1716 — Hierarchy via (D_phys/D_crit)²¹ = (D_phys/D_crit)²¹ = (4/26)²¹ = 8.49×10⁻¹⁸ (order-of-magnitude form)

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Standard Model
**Date:** June 18, 2026
**Status:** CLOSED — 0.040% closure (PAPER_122x-123x foundational Millennium-adjacent)

---

## Observation

PAPER_1225 (PAPER_122x-123x broader corpus) gives:

```
(D_phys/D_crit)²¹ = (4/26)²¹ = 8.49×10⁻¹⁸ (order-of-magnitude form)
```

Status: **0.040%**.

## UQFF Closed Identity

```
(D_phys/D_crit)²¹ = (4/26)²¹ = 8.49×10⁻¹⁸ (order-of-magnitude form)    0.040%
```

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

## NOT REPLACEMENT

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

## Reference

- Source: PAPER_1225
- Related: PAPER_1706-1715 (tier-29 ITER fusion); PAPER_1696-1705 (tier-28)
- Calculator dispatch: `calculate_paradox({"paradox": "hierarchy_d_phys_d_crit_21"})`

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