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    "assumptions": "Let A ⊆ B(Hₐₜ) be the fixed unital C*-algebra obtained by adjoining the chosen shell-link unitaries to the atomic representation of the CAR algebra C, and then taking the norm-closed unital *-algebra they generate. Let Hτ = L²(C, τC) be the GNS Hilbert space of the normalized CAR trace τC. Use the established faithful representation ρ: A → B(Hτ). No finite-dimensionality or CH hypothesis is assumed.",
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      "text": "theorem not_finiteDimensional_separableCounterexampleHilbertSpace :\n    ¬ FiniteDimensional ℂ SeparableCounterexampleHilbertSpace := by\n  intro hfinite\n  letI : FiniteDimensional ℂ SeparableCounterexampleHilbertSpace := hfinite\n  letI : FiniteDimensional ℂ\n      (SeparableCounterexampleHilbertSpace →L[ℂ] SeparableCounterexampleHilbertSpace) :=\n    ContinuousLinearMap.finiteDimensional\n  exact (not_finiteDimensional_shellFamilyTarget homogeneityShellFamily)\n    (FiniteDimensional.of_injective\n      (LinearMapClass.linearMap separableCounterexampleRepresentation)\n      separableCounterexampleRepresentation_injective)"
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