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In the Grassmannian formulation of the S-matrix for planar $\mathcal{N}=4$Super Yang-Mills, $N^{k-2}MHV$ scattering amplitudes for $k$ negative and $n-k$positive helicity gluons can be expressed, by an application of the globalresidue theorem, as a signed sum over a collection of$(k-2)(n-k-2)$-dimensional residues. These residues are supported on certainpositroid subvarieties of the Grassmannian $G(k,n)$. In this paper, we replacethe Grassmannian $G(3,n)$ with its torus quotient, the moduli space of $n$points in the projective plane in general position, and planar $\mathcal{N}=4$SYM with generalized biadjoint scalar amplitudes $m^{(3)}_n$ as introduced byCachazo-Early-Guevara-Mizera (CEGM). Whereas in the Grassmannian formulationresidues of the Parke-Taylor form correspond to individual BCFW, or on-shelldiagrams, we show that each such $(n-5)$-dimensional residue of $m^{(3)}_n$ isan entire biadjoint scalar partial amplitude $m^{(2)}_n$, that is a sum overall tree-level Feynman diagrams for a fixed planar order. We propose ageneralization which would give rise to identifications of $m^{(2)}_n$ inside$m^{(k)}_n$ for $k\ge 4$, via $(k-2)(n-k-2)$-dimensional residues. Our prooffor $k=3$ uses the CEGM formula for $m^{(3)}_n$; it predicts a new Minkowskisum realization of the associahedron in terms of certain positroid polytopes inthe second hypersimplex $\Delta_{2,n}$.

Biadjoint Scalars and Associahedra from Residues of Generalized Amplitudes