Mohammad Reza Rahmati
Higher Polylogarithmic Identities on Configuration Spaces $M_{0,7}$ and $M_{0,8}$.
We extend a residue--theoretic approach to polylogarithmic identities
from six points to seven and eight marked points on the projective line. Using the cluster
geometry of $\overline{M}_{0,n}$ and canonical logarithmic top forms, we construct
seed--independent cohomology classes on $\overline{M}_{0,7}$ and $\overline{M}_{0,8}$ and
analyze their boundary behavior. We show that their residues factor through lower--point
moduli spaces and that the global residue theorem yields universal relations of
polylogarithmic weights four and five. These relations are naturally interpreted via the
Orlik--Solomon bi--complex and match the expected structure of the corresponding
polylogarithmic complexes. The results place the six--, seven--, and eight--point cases
into a single geometric hierarchy governed by residues, mixed Hodge theory, and cluster
structures on $M_{0,n}$.
