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A 1975-77 would have had the oval decal which would have had the serial number and "Made in USA" on it. Could the guitar have been refinished? Does it look like the electronics have been worked on? Seems like a kinda big spread for the pot codes. How about a photo of the control cavity. Also, include some overall shots of the guitar.
I see some kind of impression into the wood on the back of the headstock where the serial # would reside . My gut tells me the ink dried out and vanished .
I sold a LP many many years ago. Long story short, it was nearly new and hardly played. The buyer was a musical instrument shop, and the man who inspected it questioned if the headstock had ever been repaired (broken). He said when that happens, sometimes the overspray washes out any markings on the back, and the serial number was barely visable. This was pretty much a new guitar so that wasn't the case. It took some convincing and letting him look at it 10 ways in all different directions before he believed me.
My guess is that the serial number is there, it's been obscured by the weather checking and playing wear & tear.
Do you have the guitar or just the pictures?