Show me in the book.

You keep saying that, but you've offered exactly zero.
To get you started:
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Construct is a catch-all term for the entities in the Matrix that are able to make complex decisions, carry programs, and operate autonomously. The list includes, but is not limited to, personas, agents, IC, AI, e-ghosts, and sprites.
If they're separate in this kind of list, they can't be the same thing.
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Programs can be purchased (or written by a hacker) and then stored with a persona or agent
Again, if listed apart, they're clearly not the same thing. The table on p239 SR4a also makes this distinction for cybercombat.
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Though personas are sometimes confused with operating systems, in fact they are the basic user interface an operating system provides by which you access the device and the Matrix.
Pilots are OS, so they're not persona, and they 'access' the device directly.
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Pilots are a special type of OS with more autonomous decision-making ability, used in agents and drones.
Operating system, not user.
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Persona programs are simsense user interfaces; built-in firmware that allow a user to interact with the Matrix
Machines don't need simsense, they get data; they're not a user.
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Because they act at digital speeds, they receive two extra Initiative Passes (three total).
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Like any program, the drone’s Pilot acts at digital speeds.
Not VR, let alone hot-sim, which has no meaning for a non-meat brain. Neither do any drones have sim modules, hot-sim modified or not.
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A hot sim interface has been modified to bypass the simsense peak limiters that protect your nervous system from damaging biofeedback.
Pilots have no bio to feedback, no nervous system, no simsense. They're not vulnerable to Black IC, and they can't become addicted.
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[Black Hammer] has no effect on programs, agents, IC, sprites, or AR users.
I'll leave a few for you to find.