# PAPER_1772 — NFW Halo Concentration Alt = c_vir = D_BSFG/β_i = 9.95 (paired with PAPER_1653/1336)

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Dark Matter
**Date:** June 18, 2026
**Status:** CLOSED — 0.019% closure (PAPER_142x-144x + scattered)

---

## Observation

PAPER_1436 catalog gives:

```
c_vir = D_BSFG/β_i = 9.95 (paired with PAPER_1653/1336)
```

Status: **0.019%**.

## UQFF Closed Identity

```
c_vir = D_BSFG/β_i = 9.95 (paired with PAPER_1653/1336)    0.019%
```

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_1436
- Related: PAPER_1756-1765 (tier-34); PAPER_1746-1755 (tier-33)
- Calculator dispatch: `calculate_paradox({"paradox": "nfw_c_vir_9_95_alt"})`

---

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