# PAPER_1498 — U_UA Coupling Constant = 1/SO_5⁴ = 10⁻⁴ EXACT

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Bucket A (Millennium) / Cross-domain identity
**Date:** June 17, 2026
**Status:** CLOSED — Millennium Prize UQFF coordinator constant matches Sun quiet B-field identity

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## Observation

PAPER_563 (Millennium Prize UQFF Coordinator — All Six Problems) lists the canonical UQFF calibrated constants:
- κ = 5.0e-4 day⁻¹
- [SSq] = 5.7e-1
- H_SCm ≈ 9.9e-1
- **U_UA ≈ 1.0e-4**  ← target
- k_η = 1.0e-113
- β_i ≈ 6.0e-1

## UQFF Closed Identity

```
U_UA = 1 / SO_5⁴ = 1 / 10⁴ = 1.0 × 10⁻⁴   EXACT
```

## Cross-Domain Pairing

This identity is structurally identical (in dimensionless form) to:
- **Sun quiet B-field** = 1/SO_5⁴ = 10⁻⁴ T (PAPER_1486 / F:/Aetheric Propulsion)

Same integer-primitive form, different physical domains (coupling vs. magnetic field), different units. The shared identity reveals SO_5⁴ as a recurring suppression factor across UQFF coupling and field hierarchies.

## NOT REPLACEMENT

SM has no analogue — U_UA is the UA-channel coupling specific to UQFF. The value 10⁻⁴ in SM appears only as fitted dimensionless ratios (e.g., gauge-coupling running) with no structural origin.

## Reference

- Source: PAPER_563 Millennium Prize UQFF Coordinator
- Related: PAPER_1486 (Sun quiet B-field), all 6 Millennium derivations (Bucket A)
- Calculator dispatch: `calculate_paradox({"paradox": "u_ua_coupling_constant"})`

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**Copyright** — Daniel T. Murphy, daniel.murphy00@gmail.com, June 17, 2026, Youngstown OH.
