Critical-point behavior under physical exponent specialization

Determine whether the generic critical-point degree of the affine divisor arrangement associated with the zonotopal stringy integral is preserved under the constrained physical exponent specialization, and whether a corresponding critical-point pushforward to the zonotopal correlator exists.

Background

The paper associates the zonotopal stringy integral with logarithmic critical equations on a complexified divisor complement. After passing to sign-invariant variables, the excluded loci form an affine hyperplane arrangement whose generic critical-point count can be computed from its Euler characteristic or finite-field characteristic polynomial.

The generic degree is obtained by treating the logarithmic weights of the arrangement hyperplanes as independent and generic. In the physical correlator, however, the exponents are constrained by the site and edge energies, including relations such as the definition of the site partial energies. The paper does not establish whether the generic arrangement-theoretic degree survives this specialization or whether the resulting physical critical points admit a pushforward representation yielding the zonotopal correlator.