All Numenta algorithms biologically-constrained. All aspects of the SP / TM computations can be traced back to neuroscience. For neuroscience resources supporting Spatial Pooling, see Why Neurons Have Thousands Of Synapses, A Theory Of Sequence Memory In Neocortex.
We are doing theoretical neuroscience. We don’t care about the computational expense, we want to know how the brain is working. Our research team is currently taking a break from neuroscience research while attempting to apply our models to current Deep Learning architectures, so we’re not focused on this at the moment.
There is a lot of information in our papers. Some of them have mathematical explanations if that is what you are looking for. And BAMI has pseudocode for encoders, SP, and TM. Lots of people have already created HTM implementations using that pseudocode. I’m not saying it is complete, but it can be done with the resources that already exist. I am working on a replacement for BAMI (see Building HTM Systems (WIP Document) - #38 by rhyolight).