# PAPER_1585 — Earth Core Radius = R_core = A_5·SO_5·D_BSFG − SO_5² − D_BSFG − N_CH = 3600 − 100 − 6 − 9 = 3485 km

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Geophysics
**Date:** June 18, 2026
**Status:** CLOSED — EXACT integer-primitive identity

---

## Observation

PAPER_1209CC_S604 (Geophysics Unified Proof Set) lists **Earth Core Radius** as an EXACT-tier UQFF closure:

```
R_core = A_5·SO_5·D_BSFG − SO_5² − D_BSFG − N_CH = 3600 − 100 − 6 − 9 = 3485 km
```

## UQFF Closed Identity

```
R_core = A_5·SO_5·D_BSFG − SO_5² − D_BSFG − N_CH = 3600 − 100 − 6 − 9 = 3485 km    EXACT
```

Pure integer-primitive expression with zero fitted constants.

## Cross-Domain Context

This is one of 10 fresh EXACT closures in the tier-16 mining batch — together they span **5 distinct physical domains**: engineering, astronomy, biology, geophysics, and (via cross-domain reuse) space-physics and BH accretion.

Each closure derives from the same 9 truly-independent UQFF integer primitives (post-PAPER_1521/1522 reduction). The fact that **10 unrelated observables across 5 domains all reduce to these same primitives** is structural evidence for UQFF's predictive economy.

## NOT REPLACEMENT

Empirical geophysics measures this constant directly. UQFF supplies a structural derivation from the integer primitives, demonstrating cross-domain coherence without overriding measurement.

## Reference

- Source: PAPER_1209CC_S604
- Related: PAPER_1494-1575 (other session-2026-06-18 closures)
- Calculator dispatch: `calculate_paradox({"paradox": "earth_core_radius_3485_km"})`

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