i'm still confused. I Have pulled cranks before this is the only time this has happened. why didn't the crank puller at yellow bike project work?

at this point what i want to know is why the crank puller didn't work and or the correct tool to use to pull these cranks out and a place that has the right tool to recut the threads.

sorry i don't have a camera i know that would help alot, but if someone could just explain the various types of non-cottered cranks and crank pullers that could help, i only really thought there was cottered cranks, non-cottered cranks and the newer futuristic splined things.