Yesterday for me, was the drastic sounding Nonconservative Neurobiology - A geometric perspective upon synaptic transmission theory.
I found full text, working on it now:
To me much of the paper you found is first saying that they detected a geometric related ratio that should be evident somewhere in the system, for it to work a certain way where in this case regardless of size the object fills the entire given memory space.
In another paper for readings from live rats navigating a 2D environment there was a noted ratio. My best guess model for the navigation system they were recording from ended up having the same ratio as live animal experiments, being caused by the signal geometry of a noise free 2D wave propagating in a hexagonally interconnected network. Each place in the network would otherwise not be simply passing signals coming in one direction from neighboring places to neighbors on opposite side, none of which passed a wave signal in and must not be sent a signal back out or there is chaos instead of single wave radiating out from a single point.
Here is the video for the paper you have, starting where there is mention of a ratio where there is agreement between their model (from what I can see based on electrode array readings) of a population of neurons, and single neuron readings using their glass tube electrode.
Although I’m not exactly sure how the two are mechanistically related to each other in this video Jeff speaks about scaling of columns here:
What helped get me excited yesterday was seeing the illustration shown below, from the Nonconservative Neurobiology theory that at the synapse level proposes a vesicle-friendly way to branch out a hip bone connecting to a leg bone, or fine features of a cup.
After spending time studying what got you excited it looks to me like what is contained in “critical branching networks” may fractal down to something like this. That’s my best guess for right now, anyway.