OAI/GroupTheory/PolycyclicRecognition/Geometry/CartanStationaryTemplateComparison.lean

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1 declarations, 0 contain sorry, 0 declared as axioms

Actual stationary template-volume comparison

The lower count uses independently sampled coordinates of the actual root factor. The upper count uses the image paths in the ambient group. No volume-comparison statement is assumed as an input.

  1. theorem OAI.PolycyclicRecognition.CartanWordModel.exists_template_exponent_le_of_stationary_mean line 50

    Source documentation

    Stationary averaging and actual path packing bound the exponent of the box supported by any prescribed finite family of Cartan directions.

    theorem exists_template_exponent_le_of_stationary_mean
        (hExp : IsGroupExponential Exp)
        (realize : ExponentialLinearRealizationInput (EG := EG) (G := G))
    …

    Mentions: OAI.PolycyclicRecognition.ExponentialLinearRealizationInput