 144/-! ## Recognition Dimension -/
 145
 146/-- The recognition dimension at a point is the dimension of any chart containing it -/
 147def hasRecognitionDimension (c : C) (n : ℕ) : Prop :=
 148  ∃ φ : RecognitionChart L r n, c ∈ φ.domain
 149
 150/-- **GEOMETRY AXIOM**: Dimension is well-defined.
 151
 152    **Status**: Axiom (invariance of domain)
 153    **Justification**: Brouwer's invariance of domain theorem
 154    **Reference**: Standard topology; Mathlib.Topology.Basic -/
 155def recognition_dimension_unique_hypothesis
 156    (φ : RecognitionChart L r n) (ψ : RecognitionChart L r m) (c : C) : Prop :=
 157    c ∈ φ.domain → c ∈ ψ.domain → n = m
 158
 159theorem recognition_dimension_unique
 160    (φ : RecognitionChart L r n) (ψ : RecognitionChart L r m)
 161    (c : C) (hφ : c ∈ φ.domain) (hψ : c ∈ ψ.domain)
 162    (h : recognition_dimension_unique_hypothesis (L := L) (r := r) φ ψ c) :
 163    n = m :=
 164  h hφ hψ
 165
 166/-! ## Finite Resolution Obstruction -/
 167
 168/-- **Key Obstruction Theorem**: If a neighborhood has finite resolution but
 169    infinite configurations, no recognition chart can exist on that neighborhood.
 170
 171    This is the fundamental tension: discrete recognition geometry cannot
 172    smoothly embed into continuous Euclidean space. -/
 173/-- **GEOMETRY AXIOM**: Finite resolution prevents charts on infinite sets.
 174
 175    **Status**: Axiom (cardinality/pigeonhole argument)
 176    **Justification**: Can't inject infinitely many points into finite image
 177    **Reference**: Recognition Geometry paper, Obstruction Theorem -/

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