{"id":"openai-math/A-finite-Smith-Toda-complex-V4-at-the-prime-1009","pdf":"https://github.com/openai/math/blob/main/preprints/A-finite-Smith-Toda-complex-V4-at-the-prime-1009-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-finite-Smith-Toda-complex-V4-at-the-prime-1009-September-23-2026","tags":["stable-homotopy","algebraic-topology","chromatic-homotopy"],"score":0,"title":"A finite Smith–Toda complex V(4) at the prime 1009","domain":"Topology","family":"308","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GT","summary":"We construct a Smith–Toda complex $`V(4)`$ at the prime 1009. It is an ordinary finite 1009-local spectrum whose Brown–Peterson homology is $`BP_*/(1009,v_1,v_2,v_3,v_4)`$, with its canonical comodule structure and generator in degree zero.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-23","reactions":{},"discussion":[{"url":"https://arxiv.org/abs/2610.23215","date":"2026-10-16","kind":"web","site":"arXiv.org","text":"We show that the Smith-Toda complex V(4) exists for all primes p >= 11. This improves on the recently announced result by OpenAI that V(4) exists at the prime 1009.","added":"2026-10-24","title":"The Smith-Toda complex V(4) exists for p >= 11","author":"Vigleik Angeltveit","record":"arxiv/2610.23215"}],"formalized":false,"family_title":"Finite Smith–Toda complexes at every height"}