Enumerates all (k, L) pairs where k = odd steps and L = even steps in a candidate cycle. Shows that any cycle in [2, 10^12] would require k >= 26 odd steps. Combined with Simons & de Weger (2005): no ...
Collatzscape is a reproducible implementation of a forced complex dynamical system: This function is harmonic outside the Julia set and yields the exact electrostatic potential analog for our particle ...
Google released an upgraded Gemini 3 Deep Think on Wednesday that solved 18 previously unsolved research problems across mathematics, physics, and computer science. Announced February 12, this major ...
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