As an ex-failure analysis and electron microfractographer (SEM and TEM), I can definitely say it is broken. Nice last photo.
Valves are made by hot upsetting the head shape on the end of a steel bar. Axial forging might be a good description. Several additional operations result in the finished valve. The grain of the metal spreads out from the center to the edge of the disk. The machined valve seat exposes the end grain to the hot gasses. End grain is the most susceptible to corrosion and erosion.
The applied stresses on a valve head rim are complex and not intuitive for me to understand. The erosion pits around the entire seat indicate that the valve may not have been seating in the head for a long time. The hot gasses were carving out seat material with every stroke. Some spot decides to be worse than the others. Nature finds the weak link.
The fracture can open but not fully fail for some time. During this period, the fracture face is exposed to the hot environment and becomes dark. The dark area at the seat on the right side is the most likely origin of the fracture. Microscopic fracture analysis is not possible since the fine detail is smoothed over by the hot gasses. I can make out two dark arcs as the fracture spread through the uniformly thick portion of the valve head. The thickness began to increase as the crack moved toward the center of the valve, the crack then turned back toward the rim. The angle of the fracture plane also changed to 45 degrees relative to the original plane of fracture. This often called the shear lip. This is the rapid part of the fracture.
None of this may be true, but it has been well imagined. (Arthur Clarke)
Roy
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