# PAPER_1601 — Pine Wood Density = ρ_pine = SO_5²·D_phys + SO_5² = 400 + 100 = 500 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_S570 (Engineering Unified Proof Set) lists **Pine Wood Density** with the integer-primitive expression:

```
ρ_pine = SO_5²·D_phys + SO_5² = 400 + 100 = 500 kg/m³
```

Residual: **EXACT**.

## UQFF Closed Identity

```
ρ_pine = SO_5²·D_phys + SO_5² = 400 + 100 = 500 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_S570
- Related: PAPER_1494-1595 (other session-2026-06-18 closures)
- Calculator dispatch: `calculate_paradox({"paradox": "pine_wood_density_500"})`

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