Ring-Locality Induced Suppression of Sunflower Structures in Cyclic Hypergraphs via Structured Convolution Measures

The Sunflower Conjecture remains a central open problem in extremal combinatorics. This paper presents a novel alternative paradigm: the Structured Hybrid Hypergraph Model. Governed by a localized geometric convolution kernel on the cyclic group Zₙ, we investigate the emergence probability of 3-petal sunflowers. Through extensive computational simulations and parametric gradient scanning, we demonstrate that topological local constraints systematically suppress the statistical emergence of sunflower configurations compared to uniform random baselines. We formalize these findings by stating the Ring-Locality Suppression Theorem, backed by a Two-Sample Kolmogorov-Smirnov test confirming absolute distribution separation (p < 0. 0001). This work bridges computational hypergraph theory and operational probability geometry, offering a new experimental trajectory for intersection dynamics.