How Far From Schwarzschild Can the Two Shadows Be? Deviation Bounds From Diameter Alone

Define the fractional deviation delta as the observed shadow diameter divided by the Schwarzschild diameter predicted from an independent mass and distance, minus one. For M87*, delta is +0.058 with a combined width of 0.138; for Sagittarius A*, using the inferred shadow, delta is -0.086 with a width of 0.144, while using the emission ring instead would give -0.027, shifting delta by about six hundredths purely by a choice of definition. At two standard deviations the diameter data alone bound any spherically symmetric departure from the Schwarzschild shadow scale to 0.33 for M87* and 0.37 for Sagittarius A*. Those are the honest widths of the test. Geometries predicting deviations inside them, a class that includes many regular-black-hole and modified-gravity models at plausible parameter values, are not constrained by shadow size at all, whatever their other merits. Computed from published values; simulated, not measured.