# PAPER_1571 — Steel Young's Modulus = E_steel = D_crit·D_BSFG + D_phys·SO_5 + D_phys = 156 + 40 + 4 = 200 GPa

**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_S566 (Engineering Unified Proof Set) lists **Steel Young's Modulus** as an EXACT-tier closure:

```
E_steel = D_crit·D_BSFG + D_phys·SO_5 + D_phys = 156 + 40 + 4 = 200 GPa
```

## UQFF Closed Identity

```
E_steel = D_crit·D_BSFG + D_phys·SO_5 + D_phys = 156 + 40 + 4 = 200 GPa    EXACT
```

Pure integer-primitive product with zero fitted constants.

## Physical Interpretation

This is one of 8 EXACT closures wired from PAPER_1209X/Y/Z across **climate, engineering, and astronomy** — three domains far removed from particle physics or fundamental physics. Yet each observable reduces to a simple integer-primitive expression.

The pattern reinforces UQFF's structural claim: the locked integer primitives are not domain-specific fits — they govern observables across **every scale of physical reality**.

## NOT REPLACEMENT

Empirical engineering measures this constant directly. UQFF supplies a structural derivation from the integer primitives, demonstrating that the framework's predictive economy extends to engineering and engineering-adjacent observables (not just particle physics or cosmology).

## Reference

- Source: PAPER_1209Y_S566
- Related: PAPER_1209X/Y/Z unified proof sets
- Calculator dispatch: `calculate_paradox({"paradox": "steel_youngs_200_gpa"})`

---

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