Block Balance and Saturation Certificates for Cyclic Root Degenerations
Year: 2026
Type: preprint
Abstract: We study boundary points of the reciprocal bilinear system associated with cyclic roots. For an arbitrary actual support pattern, we give a localized elimination that retains all kernel coordinates and identifies the saturated local equations. At the coordinates where both limiting vectors vanish, the two residual linear spaces are orthogonal complements for a signed pairing. Every coordinate block that splits one of these spaces must contain equally many time and frequency coordinates at a genuine boundary point. We prove this condition by constructing an explicit polynomial whose product with the common bilinear parameter lies in the original ideal. A cyclic order-ten example exhibits an unbalanced block despite satisfying the global support counts. Explicit square-order families show why intermediate vanishing rates must be retained.
Author: Liang, Jiahui
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225664109
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