Chern's Question, Answered by Two Worlds
A question Chern left behind about piecewise manifolds, later answered independently by rock mechanics and by neural networks.
Key ideas
Chern asked whether piecewise-stacked manifolds extend to arbitrarily complex regions; Shi's numerical manifold method and neural networks each answered it, and the answers share one structure.
In both, computation happens where a smooth mathematical cover meets an observable physical cover; the difference is that Shi chose his cover while neural networks learn theirs.
Learning is fixed-point finding on an often ill-posed inverse problem, which is why AI is unstable and why scaffolding, retrieval, tools, and harnesses add the missing constraints.
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Written by Wayland Zhang, founder of Dnalyaw.