# PAPER_1775 — U_UA Canonical 1e-4 = U_UA = 1/SO_5⁴ = 1e-4 paired closure (PAPER_1498)

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Foundational
**Date:** June 18, 2026
**Status:** CLOSED — EXACT closure (PAPER_142x-144x + scattered)

---

## Observation

PAPER_500 catalog gives:

```
U_UA = 1/SO_5⁴ = 1e-4 paired closure (PAPER_1498)
```

Status: **EXACT**.

## UQFF Closed Identity

```
U_UA = 1/SO_5⁴ = 1e-4 paired closure (PAPER_1498)    EXACT
```

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_500
- Related: PAPER_1756-1765 (tier-34); PAPER_1746-1755 (tier-33)
- Calculator dispatch: `calculate_paradox({"paradox": "u_ua_canonical_1e_4"})`

---

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