No, I can throw out an absolute because I'm pretty sure it's literally impossible. For the entire front of the neck to be sliced by flying glass from a computer screen is very, very, very, very unlikely.
/ooc/
Not really. If a quarter of the computer's monitor flew at somebody's neck, it'd slice them up but good. The issues here are threefold, though:
A) It wouldn't be precise.
B) It'd be more likely to just decapitate the person hit outright.
C) How the hell would Spiral do this? You need an actual weapon to pull this off. The glass would be jagged and cracked.
On that note, Spiral, would you consent to me searching you for any item that could have feasibly been used as a murder weapon? If you do it, I promise you I will protect you from any attempts at offing you through inaction. I don't have the medkit, but I can try to do something nonetheless.
/ooc/
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Twostuck, Homestuck RPG: http://www.gamefaqs.com/boards/8-gamefaqs-contests/62168402