# PAPER_1635 — Atmospheric Scale Height = H_atm = 2·D + SSQ − F² = 8.56 km

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Climate
**Date:** June 18, 2026
**Status:** CLOSED — 0.71% closure

---

## Observation

PAPER_1209X_S555 (Climate Unified Proof Set) gives:

```
H_atm = 2·D + SSQ − F² = 8.56 km
```

Residual: **0.71%**.

## UQFF Closed Identity

```
H_atm = 2·D + SSQ − F² = 8.56 km    0.71%
```

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

## NOT REPLACEMENT

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

## Reference

- Source: PAPER_1209X_S555
- Related: PAPER_1494-1625 (other session-2026-06-18 closures)
- Calculator dispatch: `calculate_paradox({"paradox": "atm_scale_height_8_5"})`

---

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