# PAPER_1764 — RVB Spin Liquid Threshold = RVB threshold = Φ_5/6 × β_i = 0.502 (same primitive product as f_bar)

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Condensed Matter
**Date:** June 18, 2026
**Status:** CLOSED — 0.7% closure (PAPER_132x-135x astrophysics + condensed matter)

---

## Observation

PAPER_1350 (PAPER_132x-135x corpus) gives:

```
RVB threshold = Φ_5/6 × β_i = 0.502 (same primitive product as f_bar)
```

Status: **0.7%**.

## UQFF Closed Identity

```
RVB threshold = Φ_5/6 × β_i = 0.502 (same primitive product as f_bar)    0.7%
```

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

## NOT REPLACEMENT

Standard frameworks address this differently. UQFF supplies a structural integer-primitive form.

## Reference

- Source: PAPER_1350
- Related: PAPER_1746-1755 (tier-33); PAPER_1736-1745 (tier-32)
- Calculator dispatch: `calculate_paradox({"paradox": "rvb_threshold_0_506"})`

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