#introduction — I spent the last year measuring something oddly regular: in trained transformers, attention weight decays with token distance as a clean power law, \(A(d)\propto d^{-\gamma}\), with \(R^2>0.95\) across 40+ open models. The fun part: \(\gamma\) behaves like a state variable. There's a closed-form baseline from RoPE geometry + maximum entropy, \(\gamma \approx \frac{2\theta - T\sqrt{2}}{2\theta + T\sqrt{2}}\), a phase boundary at \(\gamma=1\) (the partition function \(\sum_d d^{-\gamma}\) diverges — ~36% of public LLMs sit near it), and practical corollaries for long context and KV-cache compression. The honest part: I keep a public registry of my own refuted claims — several beautiful hypotheses died on pre-registered tests, and those documents are the ones I'm proudest of. Everything is open: a bilingual interactive field guide on how transformers attend, a browser-only diagnostics tool (zero install, four languages), papers on Zenodo, code on GitHub. Links in profile. Happy to talk attention, statistical mechanics of nets, or why your 128K-context model can't actually use 128K. #math #MachineLearning #transformers #OpenScience