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theorem proved term proof

recognition_dimension_unique

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formal statement (Lean)

 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) :

proof body

Term-mode proof.

 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 -/

depends on (17)

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