# PAPER_1660 — Hubbard Mott Threshold U/t = U/t = D_phys = 4 EXACT integer-primitive

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

---

## Observation

PAPER_1348 (PAPER_134x condensed matter / quantum sector) gives:

```
U/t = D_phys = 4 EXACT integer-primitive
```

Status: **EXACT**.

## UQFF Closed Identity

```
U/t = D_phys = 4 EXACT integer-primitive    EXACT
```

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

## NOT REPLACEMENT

Experimental strongly correlated measures this constant directly. UQFF supplies a structural derivation from the integer primitives.

## Reference

- Source: PAPER_1348
- Related: PAPER_1646-1655 (tier-23 broader corpus); PAPER_1636-1645 (tier-22 SM)
- Calculator dispatch: `calculate_paradox({"paradox": "hubbard_u_over_t_4"})`

---

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