{"id":"openai-math/A-rational-obstruction-to-strong-chromatic-splitting-at-height-three","pdf":"https://github.com/openai/math/blob/main/preprints/A-rational-obstruction-to-strong-chromatic-splitting-at-height-three-September-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-rational-obstruction-to-strong-chromatic-splitting-at-height-three-September-25-2026","tags":["stable-homotopy","chromatic-homotopy","algebraic-topology"],"score":0,"title":"A rational obstruction to strong chromatic splitting at height three","domain":"Topology","family":"318","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GT","summary":"For every prime p ≥ 5, the canonical map $`L_0L_{K(3)}S\\to L_0L_{K(2)}L_{K(3)}S`$ for the sphere spectrum S is nonzero on π −3 . Consequently, the height-three strong chromatic splitting formula is false in this range, even as an equivalence of underlying $`E(2)`$-local spectra without specified summand maps.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"Chromatic splitting: filtrations and counterexamples"}