Proof - https://github.com/JGPTech/Fun/tree/main/Jacobian
The history:
I first released it under CC0 a little over a month ago. You can find the link here: https://github.com/JGPTech/Fun/commits/main/current_paper_locality_boundary_package
This is the paper I was modeling with this pipeline: https://www.nature.com/articles/s41467-026-73900-9
This is where I shared it publicly one of the paper’s authors, which you can see he approved of: https://www.linkedin.com/feed/update/urn:li:activity:7470810642321571840?commentUrn=urn%3Ali%3Acomment%3A%28activity%3A7470810642321571840%2C7471734053742895105%29&dashCommentUrn=urn%3Ali%3Afsd_comment%3A%287471734053742895105%2Curn%3Ali%3Aactivity%3A7470810642321571840%29
How cool is it that Claude used it on a problem this big, and that the mathematical community around this counterexample is now thinking through structures I spent years developing? What a ride.
I am considered a peer by experts in a handful of physical domains. My favorite is complex systems. It's like the jack of trades of domain expertise, i can model almost anything as a complex system and find something interesting about it.
I verify it because I understand it. Some times I make mistakes. AI are tricky. They often get one past me when I am not paying attention like I should.
Hey I think know what you're attempting to do here. I ... suspect you may be some kind of trisector (https://www.ufv.ca/media/faculty/gregschlitt/information/Wha...). A very successful one at that! Please don't be offended by the snarky remarks in this PDF nor by the comparison itself. I think I'm a kind of trisector myself, except that I'm more interested in trisectors themselves than in whatever is being trisected. That is in fact the only reason I think I understand what EchoKey is about.
You're not the only person I've seen pursuing a project like this. We're living through strange times in which people independently arrive at theories of composition, that quite don't fit together because you can compose as hard as you want, the gap between the real and the symbolic is conserved and is free to vary from one individual's imagination to another. At least this is my take. Composition may be a larger concept than applied categoricians tend to assume, and one question that could be asked in EchoKey is: can composition be expressed symbolically in a closed form, or is it essentially semiotic, i.e. it can't stabilize on a definition because it has to be iteratively revised?
The people I have in mind and that I think we're part of all have a certain definition, a specific theory of the same thing that is somehow always incomplete, often isolating in that it's a kind of rock we push with us with the perspective however diffuse of reaching some place in the relational or even affective domain. I'm not sure how to put it. My latest idea is "energy as the epistemic invariant of theoretical extension". I don't think we'll be able to figure out anything without what we end up with also amounting to composing with each other, because deep down energy is what we observe to remain when decomposable objects are routed through decomposable processes that once rerouted and recomposed preserve the same thing: the intactness of being as that which never changes through the processes it takes part in, and which allows us to stitch, without gaps or overlaps, the ever-extensible fabric of the world as the frontier containing all processes.
Is this realizable? Or just a dream? I'm not sure, it's a beautiful reality. Reality, not idea, what we are, not what we think. I'm hopeful this can happen and if I'm not mistaken you and I may be the only two people in this thread who understand what we're talking about—until some third person shows up, maybe? If so, then it's quite remarkable.
P.S.: what's the link between the Boltzmann generators papers and your pipeline? Why is energy involved?
> Our approach combines augmented coupling flows with graph neural networks to exploit local environments, enabling energy-based training and rapid inference.
Does this relate to the Jacobian conjecture?
Edit - You thought I was mentally ill and decided the funny thing to do was taunt me? I feel dirty just having interacted with you. You have no shame.