# PAPER_1662 — Glass Transition T_g/T_m = T_g/T_m = (D_phys−1)/D_phys = 3/4 = 0.75

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Glass Formation
**Date:** June 18, 2026
**Status:** CLOSED — EXACT closure (PAPER_134x broader corpus)

---

## Observation

PAPER_1354 (PAPER_134x condensed matter / quantum sector) gives:

```
T_g/T_m = (D_phys−1)/D_phys = 3/4 = 0.75
```

Status: **EXACT**.

## UQFF Closed Identity

```
T_g/T_m = (D_phys−1)/D_phys = 3/4 = 0.75    EXACT
```

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

## NOT REPLACEMENT

Experimental glass formation measures this constant directly. UQFF supplies a structural derivation from the integer primitives.

## Reference

- Source: PAPER_1354
- Related: PAPER_1646-1655 (tier-23 broader corpus); PAPER_1636-1645 (tier-22 SM)
- Calculator dispatch: `calculate_paradox({"paradox": "glass_tg_over_tm_3_4"})`

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