A US federal judge has ordered a California woman accused of spying on Taiwanese President Lai Ching-te's son to stay in jail, a sign that American prosecutors are treating the case as serious Chinese state activity on US soil.

• Wanying Zhang, a 34-year-old real estate agent from Irvine, was arrested at Los Angeles airport and charged with acting as an unregistered foreign agent.
• Prosecutors called her a secret agent of a hostile foreign power, accused of tracking Lai's son and family on orders from Chinese officials.
• The flight-risk case rested on 29 trips abroad in 12 years, family and business ties in China, a missing Chinese passport, and a one-way ticket home at the time of arrest.
• Her bank account in China once took in $190,000 from an unregistered crypto trading operation, and she still has hundreds of thousands of dollars available there.
• An offer to post more than $1.2 million in property failed after prosecutors showed she declared only one home while owning several.

Outlook: Zhang stays in custody as the case moves toward trial, and an unnamed suspected accomplice who already left for China on a one-way ticket is unlikely to face US court.