In reality, is the spot price of a publicly-traded stock determined by a central algorithm as a best guess?

Every resource I’ve read about how a publicly-traded stock’s spot price is determined says that supply and demand is a major component but not the whole pie. I’ve read about naked shorts (which are now illegal among stocks but apparently still exist in practice in other dubious manifestations) and how counterfeit shares can affect spot price. I’ve read about short ladder attacks that can apparently "trick algorithms" into driving a spot price down. And I’ve read other things as well.

That said, when someone sees a publicly-traded stock’s spot price as $1.25, for example, is that number identical across all other brokers in real time? Does that mean then that a central algorithm is computing the spot price as a best guess of what it thinks the market value actually is? And if so, what sorts of things are also considered in this algorithm and how transparent is it? Because nothing I’ve read from authoritative sources says that it’s entirely supply and demand.