- Cartan(as the mathematician whose generalized spaces are referenced)
- Élie Cartan was a French mathematician who developed new ways of understanding curved spaces and geometry; his work allows us to describe spaces that bend and twist in complex ways.
- Conformal equivalence class(as the set of related geometric forms)
- A group of different geometric shapes that all have the same angles as each other, even if their sizes differ; they're all equivalent in terms of angle-relationships.
- Conformal geometry(as the mathematical field being discussed)
- The branch of mathematics that studies shapes and spaces while focusing on preserving angles, even when sizes change.
- Curvature(as the geometric property being normalized)
- A measurement of how much a surface bends or curves at any given point; the more a surface curves, the higher its curvature.
- Gauge freedom(as the mathematical flexibility that can be removed)
- The ability to describe the same physical situation in multiple different ways without changing what's actually happening; like choosing different coordinate systems to measure the same thing.
- Generalized spaces(as the type of mathematical structure being discussed)
- Mathematical descriptions of spaces that can have curves and bends in them, going beyond simple flat geometry like you learn in high school.
- Intrinsic(describing the kind of continuities that ground identity)
- Something that belongs to or is part of something by its very nature, rather than coming from outside or being relational.
- Normalization condition(used in physics and mathematics)
- A rule or constraint that you set up to make sure your mathematical or scientific framework works properly—it's like setting a standard so everything measures consistently.