"Serbia mobilized before answering the ultimatum and rejected the key demand."
No.
Just, "No."
Serbia accepted Austria's first two demands and *suggested* that Austria's third demand be submitted for arbitration.
Austria didn't even reply, save to say that Serbia's response was inadequate, and Austria certainly didn't attempt to negotitiate. Austria simply invaded anyway, revealing their ultimatum to be a ploy in the first place.
Serbia's acceptance of Austria's demands was so well done that Austria's chief ally Germany, in the form of Kaiser William II, said that there was now "no excuse for war."
Austria invaded Serbia anyway.
Again, I'll have the details later.
Mobilization, at the state of the art then, meant war. Each side had elaborate and rigid war plans. Once mobilization started, the movement of troops was calculated with mathematical precision. It was a war by timetable. So while the diplomats and the Keiser hoped for diplomacy to work, -- and issued praises for this or that diplomatic demarche,-- the generals computed distances and throughput of roads and said things like:
-- The enemy mobilized yesterday. If we mobilize today, we lose 10 miles inside our territory. If we mobilize tomorrow, we lose 20 miles. If we mobilize the day after tomorrow the enemy has access to our railroad grid and we lose the war. Your Majesty, you have to mobilize.
And His Majesty wrung his hands and listened.
The military doctrine of the time -- dictated by the military technology of the time -- made mobilization an effective act of war.