Comment by Intrinisical-AI

Love your project. And the mentiond metrics ΔS (semantic tension), λ_observe (viewpoint drift), and E_resonance (contextual energy) totally align with my mental model.

Also loved your phrase: "kind of like how meaning resists compression when you flatten it too early." That's a key point. Implicit in that is the assumption that flattening will eventually happen — and I agree (assumed for efficience in last term): Just like how we create flat maps of the Earth sometimes a flat projection is useful _as long as_ we understand the properties of the deformation and the underlying surface. If we don't, EEUU might seem a lot bigger than it's "represented", in our euclidean view.

That interpretation really clicks for me.

I'm currently exploring *geodesic-aware training methods for IR*, based on contrastive / triplet loss. Take a look if you're curious: [https://github.com/Intrinsical-AI/geometric-aware-retrieval-...](https://github.com/Intrinsical-AI/geometric-aware-retrieval-...)

Still recent and (very) experimental — but already done some initial tests. The goal is to construct a differentiable graph over the embedding space and propagate training signals end-to-end. Lots of work ahead, but preliminary results are promising (and adjusting things with o3 feedback ofc).

Are you open to collaborating or jamming on this? Would love to sync up — are you on Discord or Slack?

Thanks again for pushing this forward.