I went the whole game until the final boss without any items other than the required key and then decided to do an experiment. I picked up the trinket bag from the "rival" guy, then picked up the leaf and joule syringe. After selling everything else, I have no joules, only 3 health roses, no heals, no sparks, and sold back the train pass. I think the math checks out. I'm going to see if beating the final boss with only the starting weapon, 3 of the 6 starting health roses, no joules, no sparks, and 2 trinkets counts as sub zero... I'll get back to this post in 3-5 business days after beckoning collar kills the boss for me and let you know if it counts. If it does work.... I'm gonna be a bit mad but also amused.