Since I have accidentally stumbled into the Any% category, I have a question about the Any% rules. Specifically, what is a linear warp?

From the Any% rules (emphasis mine): Can warp to any Dimension at anytime except for linear warps from stages 3, 7 and 15.

I searched around for more info about this but couldn't find anything. Anyone have more details?

Because 4th dimension can be reached many times throughout the whole play. Therefor, for a 100% played 4th dimension, you need to get the 2 stones (1 in stage 1 and the 2nd in stage 2) to be able to warp after the bonus stage (Stage 3). This way, you'll fully cover the 4th dimension and have it as a complete 4th dimension run. reaching 4th dimension any other way would have you miss earlier 4th dimension stages. You can view my run to know how to warp earliest possible.

Linear warping stages 3-7-15 means you warp as early as possible and you keep warping when earliest possible to 4th dimension. If you do this linear warp, you fall into 4th dimension category.

Ah, in that case my Second Dimension runs are invalid. I'll delete them.