To be honest I find the prosecutions theory to be just as far fetched as any speculation mentioned on these forums.
It takes 20 mins to walk from his house to where its said that he was seen by Andrina Bryson. To be there he would have to have dropped everything he was doing and ran out the door after the first txt to be at the Easthouses end of the path. The first txt was 16.34 the last was 16:38, AB's sighting was 16:54.
It takes 8-10 mins to get from there to the murder site so that take us up to 17:02 - 17:04.
Luke calls Jodi house phone at 17:32 and again at 17:40. This leaves 33 mins to commit the murder.
Luke is allegedly seen at 17:45 by Rosemary Walsh and Lorraine Fleming at the Newbattle end of the path.
It takes 8 mins to get from the Newbattle entrance to the path to the entrance to Luke's street where we was positively identified at 17:50 - 18:00 by the boys on the bikes who knew him and described the clothes he had on as the same as he wore to school that day and these were the same clothes that he was wearing when he was arrested.
Where is the time for him to run home throw a bloody parka at his mum, tell her whats happened and ask her to burn it, clean himself up, then ran back out to be at the wall where he was seen by the boys then spent the evening with friends? There's no time for that to have happened.
It makes far more sense that Andrina Bryson and Fleming and Walsh were mistaken and Luke left home at 17:30 like he claims.