Year: 2026
Type: preprint
Abstract: We identify a normalization defect in a determinantal construction of fourth-order Hahn difference equations and compare its scalar equation with Foupouagnigni's 1998 elimination and its published 2001 counterpart. On an explicit positive orthogonal family, all five prescribed coefficients vanish: the formula gives \(0=0\) and imposes no condition. Along an explicit regular perturbation, division by \(\varepsilon^2\) before specialization recovers a nonzero equation on that family, the same scalar equation as the correctly executed old shift-and-eliminate procedure. On the common nondegenerate domain specified below, both constructions give the same scalar operator up to a nonzero rational factor. The first-order degree bounds follow directly from valid identities of 1998; preserving cancellations gives a bound that can be arbitrarily sharper on explicit admissible inputs, together with exact top coefficients and cancellation criteria. Explicit coefficient formulas do not by themselves yield a new scalar equation on this domain. Our comparison does not exclude corrective or expository contributions; additional computational gain or exceptional coverage must be demonstrated.
Source: arXiv (Cornell University)
Authors: Castillo, K., Gordillo-Núñez, G.
Institutions: Centro de Matemática, University of Coimbra
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222015450