Isosceles Cyclotomic Node in the Pell Family: The Case T5 = (41,41,41√2) and Comparison with the Level 24 Node
Year: 2025
Type: preprint
Abstract: This preprint develops an independent example of the cyclotomic-nodes framework, based on the family of isosceles right triangles arising from the negative Pell equation x^2 − 2y^2 = −1. We introduce a compatibility condition across three arithmetic layers: (i) the real Pell layer in Q(sqrt(2)), (ii) a Gaussian CM layer via norms in Q(i), and (iii) a cyclotomic layer via minimal inclusion in K8 = Q(zeta_8). This condition selects a nontrivial node at index n = 5, corresponding to the triangle T5 = (41,41,41sqrt(2)). Uniqueness within the symmetric subfamily with common parameter b = 5 is supported by an exhaustive SageMath verification up to |a| ≤ 10^6 (height x ≈ 10^12), with reproducible code included. We also compare this level-8 isosceles node with the previously identified level-24 cyclotomic node associated with the triangle 13–14–15, highlighting a shared structural pattern based on norm compatibilities.
Author: Méndez Ibarra, Rogelio
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7115008345
Cites:
Cited by:
Related to: