212def IsSmoothRecognitionGeometry (A : RecognitionAtlas L r n) : Prop :=
proof body
Definition body.
213 -- All transition maps are smooth 214 -- (This requires additional structure on how charts relate) 215 True -- Placeholder; full definition needs differential structure 216 217/-- **Physical Interpretation**: Spacetime is a smooth recognition geometry. 218 219 The 4 dimensions of spacetime represent 4 independent ways that 220 physical recognizers can distinguish events: 221 - 3 spatial dimensions (where) 222 - 1 temporal dimension (when) 223 224 These are recognition dimensions, not pre-existing geometric facts. -/ 225/-! **Spacetime Interpretation**: Spacetime is a smooth recognition geometry. 226 The 4 dimensions represent 4 independent ways recognizers distinguish events. -/ 227 228/-! ## The Local-to-Global Principle -/ 229 230/-! 231Local-to-global principle (documentation / TODO). 232 233Intended claim: if the atlas covers every point, then the quotient space is locally homeomorphic 234to \(\mathbb{R}^n\). The full statement requires topology/differential geometry infrastructure. 235-/ 236 237/-! ## Module Status -/ 238
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.