Will the Houthis enter Saudi Arabia by September 20?

The articles describe a significant Houthi offensive along Yemen's Red Sea coast, including the capture of Mocha and advances toward Bab al-Mandeb, but none report actual Houthi military forces entering Saudi territory. The Houthis have struck Saudi infrastructure and trade routes, but the resolution criteria explicitly exclude bombardment, sabotage, or naval presence offshore from qualifying as 'entry.' The UN envoy's warning that the conflict's consequences 'will not remain within Yemen's borders' Aljazeera envoy suggests potential escalation, but this is speculative rather than evidence of ground incursion. The Reuters article Reuters article mentions Riyadh striking back, implying cross-border exchanges, but again, strikes do not meet the 'deliberately operate within' standard. Given the current trajectory of intense fighting near the border and Houthi capabilities, there is a meaningful chance they could cross into Saudi Arabia by September 20, 2026, but the available reporting does not establish that this has occurred or is imminent. The lack of any report of Houthi ground forces entering Saudi Arabia, combined with the high bar set by the resolution criteria, leads me to lean toward 'No,' but the dynamic situation and explicit warnings of regional spillover Aljazeera envoy prevent a confident call. I assign a probability of 0.4, reflecting a real but not dominant possibility of entry.