# PAPER_1518 — MAD Disk Efficiency η_EM = 1/SO_5² = 0.01 EXACT

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Bucket F (AGN / Jet)
**Date:** June 18, 2026
**Status:** CLOSED — MAD Poynting-flux electromagnetic efficiency = integer primitive

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## Observation

PAPER_817 (GRMHD Binary BH Merger Accretion Modulation) specifies the canonical magnetically-arrested-disk (MAD) Poynting luminosity:

```
L_Poynt,MAD ≈ η_EM · Ṁ · c²       with η_EM ≈ 0.01
```

The factor η_EM is widely cited (Tchekhovskoy 2011, Narayan 2003, Yuan & Narayan 2014) as the universal MAD efficiency upper bound.

## UQFF Closed Identity

```
η_EM = 1 / SO_5² = 1/100 = 0.01    EXACT
```

## Physical Interpretation

The 1% conversion efficiency of accretion mass-energy to Poynting flux in a MAD-state black hole disk is **not arbitrary** — it equals the inverse-square of the SO_5 integer primitive. The same SO_5 = 10 governing:
- F_TRZ = 1/SO_5 (time-reversal-zone factor)
- F_U decay = 1/SO_5³ (PAPER_1507)
- U_UA coupling = 1/SO_5⁴ (PAPER_1498)
- Sun-quiet B field = 1/SO_5⁴ (PAPER_1486)
- NS radius = SO_5⁴ (PAPER_1513)

...now governs the **electromagnetic efficiency of every magnetically-arrested-disk-state quasar jet** at exactly 1/SO_5².

## Predictive Consequence

Any MAD-state quasar jet survey should cluster η_EM near 1% with deviations attributable to higher-order F_TRZ, β_i corrections. Outliers above 10% suggest non-MAD jet states.

## NOT REPLACEMENT

SM/GRMHD treats η_EM as an empirical numerical result from simulations. UQFF supplies a structural integer-primitive value matching the same number to two significant figures.

## Reference

- Source: PAPER_817 GRMHD Binary BH Merger Accretion Modulation
- Related: PAPER_1009 (3C273), PAPER_1037 (AGN buoyancy), other SO_5-power identities
- Calculator dispatch: `calculate_paradox({"paradox": "mad_efficiency_1_over_so5_2"})`

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