# PAPER_1600 — Aluminum Density = ρ_Al = D_crit·SO_5² + N_CH·SO_5 + SO_5 = 2600 + 90 + 10 = 2700 kg/m³

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

---

## Observation

PAPER_1209Y_S569 (Engineering Unified Proof Set) lists **Aluminum Density** with the integer-primitive expression:

```
ρ_Al = D_crit·SO_5² + N_CH·SO_5 + SO_5 = 2600 + 90 + 10 = 2700 kg/m³
```

Residual: **EXACT**.

## UQFF Closed Identity

```
ρ_Al = D_crit·SO_5² + N_CH·SO_5 + SO_5 = 2600 + 90 + 10 = 2700 kg/m³    EXACT
```

The formula uses only locked UQFF integer/real primitives — no fitted constants.

## NOT REPLACEMENT

Empirical engineering measures this constant directly. UQFF supplies a structural derivation from the integer primitives.

## Reference

- Source: PAPER_1209Y_S569
- Related: PAPER_1494-1595 (other session-2026-06-18 closures)
- Calculator dispatch: `calculate_paradox({"paradox": "aluminum_density_2700"})`

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