Buell intercepts Bragg coming from Chattanooga

The invasion of Kentucky in 1862 was risky, and required a number of thigns to go right. Let's say that Buell is a little closer - not likely closeenough to take Chattanooga but close enough, say because of a lack of Murfreesboro (no Forrest raid, say he's killed at Shiloh), to notice Bragg is close and attack.

1. Perryville was pretty much a draw, but with fewer men could Bragg have lost outright to Buell - perhaps becasue TTL, Thomas doesn't just prevent a loss but causes a victory?

2. Does Bragg retreat back to Chattanooga and break off his part of the Smith attack? What can Smith do without Bragg but also without Buell - where can they get the troops to oppose Smith?

3. If Buell wins, what does he do? Go after Smith next? Or figure someone else (Rosecrans detached from Grant?) can get him and advance on Chattanooga - especially considering that Washington might order him to, not quite knowing what Smith is up to?

4. Would Bragg be replaced this early if he loses Chattanooga? Would Smith abandon his Kentucky initiative?
 
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