retrocomputing

After digging some more, looks like core rope memory is different than the magnetic core memory in your link above (seems to describe magnetic core memory instead of rope memory). Core rope memory is used for ROM while magnetic core memory is used for RAM, and they have different working mechanism.

Another form of core memory called core rope memory provided read-only storage. In this case, the cores, which had more linear magnetic materials, were simply used as transformers; no information was actually stored magnetically within the individual cores. Each bit of the word had one core. Reading the contents of a given memory address generated a pulse of current in a wire corresponding to that address. Each address wire was threaded either through a core to signify a binary [1], or around the outside of that core, to signify a binary [0]. As expected, the cores were much larger physically than those of read-write core memory. This type of memory was exceptionally reliable. An example was the Apollo Guidance Computer used for the NASA Moon landings.

Basically, 1 if the sense wire going through the core, or 0 if the wire bypass the core. You basically woven 1 and 0 manually into the rope. And yeah, it doesn't matter if the cores touch each other as long as the wires are woven correctly. This article have some wiring diagram for the core rope memory: http://www.righto.com/2019/07/software-woven-into-wire-core-rope-and.html .

Looks like there are 16 wires for each core in this module?

That's awesome. It's lasted longer than modern flash does.