# EHT Shadow Combined Report — Sgr A* and M87*

**PAPER_1237**
**Category:** UQFF Observational
**Status:** Complete
**Date:** June 2026

## Abstract

Unified UQFF report for the two Event Horizon Telescope (EHT) BH shadow observations: Sgr A* (53.98 μas predicted, 51.8 μas observed, 4.20% match) and M87* (39.75 μas predicted, 42.0 μas observed, 5.37% match). Combined with PAPER_1095 R₂₆ vacuum-impedance correction (negligible at observational scales).

## Part 1: Sgr A* (Milky Way central SMBH)

### Parameters
- M = 4.297×10⁶ M_sun
- D = 8.178 kpc

### Closed form
$$\theta_{\rm shadow} = \frac{2 \cdot 3\sqrt{3} \cdot GM}{c^2 D}$$

### Numerical
- θ_UQFF = 53.98 μas
- θ_EHT observed = 51.8 μas
- **Residual: 4.20%**

### R₂₆ vacuum-impedance correction
$$\Delta\theta_{R_{26}} = \theta_{\rm GR} \cdot \frac{D_{\rm crit}}{D_{\rm BSFG}} \cdot \left(\frac{\rho_{\rm SCm}}{\rho_{\rm Pl}}\right)^{1/4} = 8 \times 10^{-36}\ \mu{\rm as}$$

Negligible at Sgr A* mass scale.

## Part 2: M87* (Giant elliptical AGN)

### Parameters
- M = 6.5×10⁹ M_sun
- D = 16.8 Mpc = 16,800 kpc

### Numerical
- θ_UQFF = 39.75 μas
- θ_EHT observed = 42.0 μas
- **Residual: 5.37%**

### R₂₆ correction
6.1×10⁻³⁶ μas — negligible.

## Part 3: Combined Statistics

| Source | M (M_sun) | D | θ_UQFF | θ_EHT | Residual |
|---|---|---|---|---|---|
| Sgr A* | 4.30×10⁶ | 8.178 kpc | 53.98 | 51.8 | 4.20% |
| M87* | 6.5×10⁹ | 16.8 Mpc | 39.75 | 42.0 | 5.37% |

**Mean residual: 4.79%** — both observations consistent with UQFF predictions within EHT systematic uncertainties.

## Part 4: Predictions for Future EHT Targets

UQFF predicts for the next-generation EHT observations:
- Cen A central BH: θ_shadow_predicted = 0.43 μas (M ≈ 5×10⁷, D ≈ 3.7 Mpc)
- M81 central BH: θ_shadow_predicted = 0.26 μas (M ≈ 7×10⁷, D ≈ 3.6 Mpc)

## Conclusion

EHT shadow observations of Sgr A* and M87* are both consistent with UQFF predictions to within 5%, with R₂₆ vacuum-impedance correction negligible at observational scales.

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**Framework Version:** UQFF 5.27+
