Positive geometry inside the ABCT variety

Establish the existence of a positive geometry inside the ABCT variety as conjectured by Lam (Conjecture 4.10), and characterize its boundary and canonical form.

Background

The ABCT variety appears as a subvariety of a Grassmannian in the context of scattering amplitudes and CHY-type constructions. Recent work (Agostini–Ramesh–Shen) addresses related structural questions, but Lam’s conjecture posits a specific positive-geometry structure within the ABCT variety. Resolving this would extend the catalogue of known positive geometries beyond polytopes and Grassmannians and provide canonical forms relevant to physics.