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I don't think it is a universally defined concept. In fictional works, characters with high-dimensional abilities may have immunity to attacks or abilities of the same dimensionality, highlighting their superior understanding and control. However, other stories depict high-dimensional characters as vulnerable to attacks within their dimensionality, requiring them to rely on defensive techniques or alternate dimensions for protection.There were mixed responses on the site's history (as the OP somewhat mentions) on if characters that are on these conditions (4-D or above in stuff like AP and the like but still on a 3D body and similar) were immune to hax of the same dimensionality as their bodies and if not what semantics would be at play, which that tried to address.