What if the Cramér-Rao bound isn't just a limit on measurement, but rather a constraint on the structure of reality itself? I have formalized this observation into what I'm calling the Amplitude Closure (AC) Framework, and I'd like feedback from mathematicians, physicists, and scientists. The core idea: a single complex amplitude Φ:Σ×Σ→ℂ, where |Φ(A,B)|² measures the statistical distinguishability between configurations A and B, governed by four information-geometric axioms. From these, geometry, quantum mechanics, statistical mechanics, and Standard Model structure emerge as a self-consistent fixed point. A few things I want to be upfront about: Although I have a PhD in science, I am not a theoretical physicist. The bar for proof is high, and I've done my best not to overstate things. The paper distinguishes carefully between what is proved, what is derived under approximation, and what remains open. I'm also one person. The breadth of correspondence with QM, GR, the Standard Model, and statistical mechanics seems remarkably high, but it would be impossible for any single person to complete a rigorous proof. My goal was to lay the scaffolding clearly enough that others can build on it. The primary claim is this: four information-geometric axioms give rise to geometry and structures compatible with much of what we already know about physics. Ground rules for replies: 1) If you're going to critique the paper, give your single best critique, not a list. Once I've responded, feel free to move to the next one. 2) Any critique must be paired with either something you find genuinely interesting in the paper, or better yet, a proposed solution to the problem you've raised. For more dynamic discussion, join the Quai Discord (physics channel). Link in the replies Link to pre-print: zenodo.org/records/194980…
