The key difference from Euclidean geometry is that a circle of radius \(r\) has circumference \(2\pi\sinh r 2\pi r\), and volumes grow exponentially rather than polynomially: \[\operatorname{Vol}(B(r)) = \operatorname{Vol}(S^{n-1})\int_0^r \sinh^{n-1}(t)\,dt.\]
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Anthropic recently built a 100,000-line C compiler using parallel AI agents in two weeks, for under $20,000. It boots Linux and compiles SQLite, PostgreSQL, Redis, and Lua. AI can now produce large-scale software at astonishing speed. But can it prove the compiler correct? Not yet.