There is no historical or international law that supports anything China has claimed here. And they know it.
They are bluffing and the USN knows it.
Because the USN knows that to strike a US battle group 500-600 miles from their nearest mainland base in China is folly that the PLAN and PLAAF cannot back up.
If this was the Yellow Sea, it might be different. But even then the USS G Washington battle group, as little as 5 years ago, sailed within 100 miles of Bejing and conducted flight operations.
Not a single Chinese aircraft came out to play. Not one.
While that may be true, they are claiming these are CONTESTED waters.
One wonders if the following has anything to do with them starting to 'contest' that area ?
As expected, details of this national intelligence capability are closely held, but much of it is likely based on the successful implementation of the earlier Coast Watch South program.
With heavy U.S. assistance, the Philippines created a network of monitoring stations combining radar, maritime surveillance and radio/data networks that provides a real-time strategic and tactical “picture” of oceanic traffic in the Southern Philippines—the so-called Sulawesi Sea Triangle. That area is a hotbed of illicit trafficking by sea and a favored logistical trail for transnational insurgent forces that prowl the region.
When completed in 2015, the west-facing Coast Watch chain will monitor the Philippines’ Exclusive Economic Zone (EEZ), extending 200 nm into the contested Spratly Islands group.
In the future, additional monitoring chains will cover the Northern and Eastern facing portions of the country as well.