 209
 210    This is the bridge to classical differential geometry: when recognition
 211    structure is "rich enough," the quotient space looks like a manifold. -/
 212def IsSmoothRecognitionGeometry (A : RecognitionAtlas L r n) : Prop :=
 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
 239def charts_status : String :=
 240  "✓ RecognitionChart defined\n" ++
 241  "✓ chart_respects_equiv: charts preserve indistinguishability\n" ++
 242  "✓ chartOnQuotient: charts induce maps on quotient\n" ++

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.