"provably extensional" is not an established term in this context and communicates nothing about the design. I simply do not believe that this design doesn't have trivial collision issues, or that it makes efficient use of memory.
For example, take the integers 0 - 196,561, and put them into your lattice-based map. Something’s got to give. There are only 196,560 containers in the map (right?)
The only relation to the Leech group appears to be the number of slots.
When a table gets full they allocate a second one, and so on, up until 256 tables when allocations start silently failing (after exactly 50319104 allocations).
I hope OP is seriously considering what’s actually been built here, and how their interactions with whatever LLM they’ve been using really reflects that. I’m genuinely a bit concerned for them.