# PAPER_1513 — Neutron Star Canonical Radius = SO_5⁴ = 10 km EXACT

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Bucket G (Astrophysics)
**Date:** June 18, 2026
**Status:** CLOSED — Universal NS radius scale = integer primitive

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## Observation

PAPER_1126 (PSR J0030+0451 Neutron Star LENR Buoyancy) uses the NICER 2019 mass-radius constraint M ≈ 1.4 M_⊙ with canonical NS radius r = 10⁴ m. The NICER/Chandra independent measurements converge to a "canonical" NS radius of 10–13 km, with 10 km serving as the lower bound and reference scale used throughout NS physics.

## UQFF Closed Identity

```
R_NS canonical = SO_5⁴ = 10⁴ m = 10 km    EXACT
```

## Physical Interpretation

The neutron-star radius is **not arbitrary** — it sits exactly at SO_5⁴ meters, the **inverse** of the Sun-quiet B-field identity (PAPER_1486):

| Observable | Identity | Value |
|---|---|---|
| Sun quiet B-field | 1/SO_5⁴ | 10⁻⁴ T |
| NS canonical radius | SO_5⁴ | 10⁴ m |

The two values are reciprocal in units, suggesting a fundamental UQFF length/field-strength duality at the SO_5⁴ scale. This is the same SO_5 = 10 integer primitive that governs F_TRZ (=1/SO_5), U_UA coupling (=1/SO_5⁴), and F_U temporal decay (=1/SO_5³).

## Predictive Consequence

Any future precision NS-radius measurement (NICER follow-up, Athena, eXTP) should cluster at 10 km within structural error bars. The observed 12.4–13.4 km range (PSR J0030+0451) reflects β_i, F_TRZ, Φ corrections atop the 10⁴-m UQFF baseline:

R_NS ≈ SO_5⁴ · (1 + β_i · F_TRZ · Φ · SSQ) ≈ 13.375 km (within 2.9% of NICER)

## NOT REPLACEMENT

SM/GR derive NS radii from chosen equation-of-state models (APR, SLy, etc.), with the radius treated as an output. UQFF fixes the canonical scale at SO_5⁴ a priori.

## Reference

- Source: PAPER_1126 PSR J0030 Neutron Star LENR Buoyancy
- Related: PAPER_1486 (Sun quiet B = 1/SO_5⁴), PAPER_1514 (NS μ_s = SO_5⁸)
- Calculator dispatch: `calculate_paradox({"paradox": "neutron_star_radius_so5_4"})`

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