The Internet's core network, crucial for key services, lacks a clear definition, hindering Internet development and security research. This study analyzes important Autonomous Systems (ASes) and proposes a rule-filtering, top-down method to infer the Internet's core network. It identifies two core memberships: Tier-1 ASes and Regional Tier-1 ASes. Despite a gap, Regional Tier-1 ASes show potential to join the core. Our proposed core structure, unlike traditional methods that randomly select TOP-K nodes, offers improved rationality and interpretability. Historical data analysis reveals the Internet's core structure as a tightly interconnected network of large provider ASes. Despite some changes, this structure shows remarkable stability and growing influence, potentially encouraging other ASes to establish direct connections with the core ASes, accelerating the trend towards a flattened Internet structure. Furthermore, the core structure may be evolving from a majority to a more minority-centric structure.