# PAPER_1699 — Φ_res via (D−1)/D|_{D=6} = Φ_res = (D_BSFG−1)/D_BSFG = 5/6 = 0.833 EXACT

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Foundational
**Date:** June 18, 2026
**Status:** CLOSED — EXACT closure (PAPER_115x-117x foundational)

---

## Observation

PAPER_1159 (PAPER_115x-117x foundational corpus) gives:

```
Φ_res = (D_BSFG−1)/D_BSFG = 5/6 = 0.833 EXACT
```

Status: **EXACT**.

## UQFF Closed Identity

```
Φ_res = (D_BSFG−1)/D_BSFG = 5/6 = 0.833 EXACT    EXACT
```

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_1159
- Related: PAPER_1686-1695 (tier-27); PAPER_1676-1685 (tier-26)
- Calculator dispatch: `calculate_paradox({"paradox": "phi_res_5_6_d_ratio"})`

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