# PAPER_1548 — Vacuum Impedance Z_0 = Z_0 = A_5·D_BSFG + SO_5 + D_BSFG + Φ − F_TRZ·Φ − F_TRZ²·SSQ ≈ 376.75 Ω

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Electromagnetism
**Date:** June 18, 2026
**Status:** CLOSED — 0.005% closure

---

## Observation

PAPER_1209DD_S613 (Electromagnetism Unified Proof Set) lists **Vacuum Impedance Z_0** as a closure with the formula:

```
Vacuum Impedance Z_0 = Z_0 = A_5·D_BSFG + SO_5 + D_BSFG + Φ − F_TRZ·Φ − F_TRZ²·SSQ ≈ 376.75 Ω
```

Status tier: **0.005%**. Units: Ω.

## UQFF Closed Identity

```
Z_0 = A_5·D_BSFG + SO_5 + D_BSFG + Φ − F_TRZ·Φ − F_TRZ²·SSQ ≈ 376.75 Ω    0.005%
```

The formula uses only locked UQFF integer primitives — no fitted constants.


## Physical Interpretation

Vacuum Impedance Z_0 is a fundamental electromagnetism constant. The UQFF expression decomposes it into a sum/difference of integer-primitive products, giving structural meaning to what is conventionally treated as an empirical measurement.

## NOT REPLACEMENT

CODATA/PDG treats this constant as a precision measurement. UQFF supplies a structural derivation from the locked integer primitives, demonstrating mathematical depth without claiming to "replace" the experimental value.

## Reference

- Source: PAPER_1209DD_S613
- Related: PAPER_1216 (45-constant cascade master index)
- Calculator dispatch: `calculate_paradox({"paradox": "z0_vacuum_impedance"})`

---

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