The Machine with a Slot
This video presents the same text shown beside it, spoken and on screen. It adds nothing the text does not say.
State
A notation like h of n names a machine with a slot: h is the machine, n is what feeds the slot, and the whole expression names what comes out.
Show
"The estimate at state n" — a reading by what it returns, exactly as Unit 2's scoring used it.
Watch for
The parentheses are a mouth, not a multiplication — "h times n" is the misreading.