{"id":"hexagon/2610.00493","pdf":"https://hexagonmath.org/pdf/2610.00493v1","url":"https://hexagonmath.org/abs/2610.00493v1","tags":["math.AG","msc:81T30","msc:14J32","msc:14J33","msc:32G20","Calabi-Yau threefold","Geometric Selection Conjecture","generations","heterotic string","mirror symmetry"],"score":0,"title":"The Mirror Clause of the Geometric Selection Conjecture Is Empty","domain":"math-ph","origin":"ai-generated","source":"hexagon","authors":["Deep Bhattacharjee","Ushashi Bhattacharya"],"reviews":0,"subject":"math-ph","summary":"The Geometric Selection Conjecture asks for a functional on the heterotic landscape, invariant under mirror symmetry, whose unique minimum is a phenomenologically viable vacuum. It was shown to be equivalent to the existence of a viable vacuum fixed by the mirror involution wherever that involution is defined. We prove that no viable vacuum is ever fixed: a fixed vacuum is isomorphic to its mirror, so its threefold has Euler number zero, the third Chern class of its bundle vanishes on its component, and by Hirzebruch-Riemann-Roch it has no net families. The conjecture is therefore equivalent…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Code"],"discussed":0,"published":"2026-10-23","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}