OAI/GroupTheory/PolycyclicRecognition/Geometry/CartanPublishedPolarRegions.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

The actual target regions and Haar trace for a transformed polar cone

  1. theorem OAI.PolycyclicRecognition.recentered_polarSamplingTemplates line 16
  2. theorem OAI.PolycyclicRecognition.CartanWordModel.MeasuredCone.uniform_polar_regions_of_action line 44

    Source documentation

    The transformed polar geometry supplies a maximizing ideal basis and a path threshold for an already specified compatible quotient action.

    theorem MeasuredCone.uniform_polar_regions_of_action
    (hExp : IsGroupExponential Exp)
    (realize : ExponentialLinearRealizationInput (EG := EG) (G := G))
…

    Mentions: OAI.PolycyclicRecognition.ExponentialLinearRealizationInput

  3. theorem OAI.PolycyclicRecognition.CartanWordModel.MeasuredCone.exists_uniform_polar_target_regions line 141

    Source documentation

    The action, its positive pure-word trace, the maximizing target basis, and the uniform path-restriction regions all belong to one actual target quotient. The region threshold is fixed before the scale or concentration errors are chosen.

    theorem MeasuredCone.exists_uniform_polar_target_regions
    (hExp : IsGroupExponential Exp)
    (realize : ExponentialLinearRealizationInput (EG := EG) (G := G))
…

    Mentions: OAI.PolycyclicRecognition.ExponentialLinearRealizationInput