Alice was all very confused about this matter, so much back and forth in her timeline. She didn't want to believe the Doctor, because she had thought she had just found her parents, only to find out that they were 'adoptive.' So her whole life was a lie, and she was back to square one on who she was and where she came from. She hated having to start over, not knowing anything majorly important about her life, because that was all she had left to believe; her life and Jack. Everything was twisting and mutating against what she thought was logical, and things were only just breaking the ice.
"Well, what about the Goblin? The Dark Hall? What's that?! I don't think that was something that had introduced itself to my life until I was 'jumping' the Void." Alice was trying to connect all the dots she had created for herself over the course of two years, with her memory and the File. The File! There was that new page, with that long equation on it! Maybe if the Doctor looked at it, he would understand what it meant!
"Doctor! Did you see the equation? On the back of the note? Jack and I forgot about it until now, but it might have something to do with all the twists in my timeline!" She wasn't even listening to what they were discussing, just throwing in her thought before she lost it.
"You sure are a sharp child, defiantly raised by yours truly," the Doctor smiled and wiggled his bow tie. "Well! Show me this equation, and we'll see what comes of it!" Alice went and retrieved the note from Jack's desk, and handed it to the Doctor. He brought out his gadgety-thing and swept it over the paper, analyzing and calculating the equation. He hummed at the gadget and stared at the paper.
"AH!" His voice boomed so loudly that Alice jump and Jack flinched. "I know what this is! It's a blood transit, an equation with a persons DNA calculated into it so that only they can use it. This must be what they used to send you here, you and only you. There was something they didn't want following you here."
"I bet I know what it was, the goblin thing, it has always been in my memory, and it was there right before I fell through the Void!" Alice was having major memory boost, her mind felt like a new door was opening. She was starting to see her mother's face, the other Doctor's face, and the goblin face, all at once. The shocked scared her and she fell back in shock.
She was lucky though, she had fallen on a chair, looking like she was had just sat down out of spite. Jack gave her a look, but she just smiled, knowing it was better not to tell him.
"Your probably right... And with a blood transit, you have saved thus world from a terrible danger, I'm assuming. Well done! You're doing Jack's job without even realizing it!"
"Yes, because that something she needs to be proud of..."
"But... Jack... The first note, the very first... Didn't say that 'he got through?' does that mean he found another way to get to our earth?"
"That is probable, the Cybermen had developed a way of getting through, maybe he has as well... The only way to check is by monitoring the Rift. But I don't think we have to worry about it. Right Doctor?"
"... Well... That may not be true... If it did make it through the Rift, that would probably mean it was using Alice's blood transit equation, causing it to only work one time, because he could only open it once. He may come looking for you so that he can... Bring over his army, because, from what you tell me, a king will never leave his army behind while conquering a new world."