Old structures, a vanishing formula

@misc{castillo2026structures,
  title = {{Old structures, a vanishing formula}},
  author = {K. Castillo and G. Gordillo-Núñez},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20192},
  eprint = {2610.20192},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20192},
  note = {CC0},
}

TY  - UNPB
TI  - Old structures, a vanishing formula
AU  - K. Castillo
AU  - G. Gordillo-Núñez
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20192
UR  - https://arxiv.org/abs/2610.20192
AB  - 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 ε^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.
ER  -