{"id":"openai-math/Failure-of-finite-assembly-for-a-chromatic-overlap-at-the-prime-three","pdf":"https://github.com/openai/math/blob/main/preprints/Failure-of-finite-assembly-for-a-chromatic-overlap-at-the-prime-three-September-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Failure-of-finite-assembly-for-a-chromatic-overlap-at-the-prime-three-September-25-2026","tags":["homotopy-theory","chromatic-homotopy","spectra"],"score":0,"title":"Failure of finite assembly for a chromatic overlap at the prime three","domain":"Topology","family":"318","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GT","summary":"At the prime three and height three, the chromatic overlap cannot be constructed from the rational, height-one, and height-two local spheres by finitely many sums, shifts, cofibers, and retracts in the category of $`E(2)`$-local modules over the derived 3-complete sphere. This gives a negative answer to the ordinary finite-assembly question for chromatic overlaps.","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"}