I'm using BA's search to find Cathay first class space just past the AA booking window. If I search BKK->JFK then I can see as many as 4 first class seats available on CX0846 from HKG->JFK (number of seats depends on the connecting flight from BKK->HKG). This is true on many days just outside the AA booking window (for instance, I'm writing on 3/23 and I can see those seats on 3/18/17). But if I search only the segment from HKG->JFK then I consistently turn up only a single first class seat on that flight. Are there really more seats if I originate in BKK, or are those extra seats phantom space?