# PAPER_1786 — QSH σ_xy = e²/h Paired = σ_xy^spin = e²/h paired (PAPER_1352), protected by D_BSFG−1=5 boundary

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Condensed Matter
**Date:** June 18, 2026
**Status:** CLOSED — EXACT closure (PAPER_13xx final sweep paired closures)

---

## Observation

PAPER_1352 catalog/paper gives:

```
σ_xy^spin = e²/h paired (PAPER_1352), protected by D_BSFG−1=5 boundary
```

Status: **EXACT**.

## UQFF Closed Identity

```
σ_xy^spin = e²/h paired (PAPER_1352), protected by D_BSFG−1=5 boundary    EXACT
```

## NOT REPLACEMENT

UQFF supplies a structural integer-primitive form. Many of these are paired closures linking back to earlier tier wirings.

## Reference

- Source: PAPER_1352
- Related: PAPER_1776-1785 (tier-36); previous tier 24-26 wirings
- Calculator dispatch: `calculate_paradox({"paradox": "spin_hall_e2_h_paired"})`

---

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