OAI/GroupTheory/PolycyclicRecognition/Analysis/LinkedProbeOffset.lean

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1 declarations, 0 contain sorry, 0 declared as axioms

1. theorem OAI.PolycyclicRecognition.MeasuredProbeRegions.offset_nonpos_of_linked_probe_bounds line 38

   Source documentation

   Insert the three actual linked chains into the independent-quotient volume comparison. The first and third chains supply the image paths; the second supplies the retained anchor profile. All profiles retain their original center, and their common error is derived from the chain bounds.

   theorem MeasuredProbeRegions.offset_nonpos_of_linked_probe_bounds
       (π : N →* Q) (hπ : Continuous π)
       (μQ : Measure Q) (μI : Measure π.ker) (μ : Measure N) (ν : Measure D)
       [SFinite μQ] [SFinite μI] [SFinite μ] [SFinite ν]
       [μQ.IsMulLeftInvariant] [μ.IsMulLeftInvariant] [ν.IsMulLeftInvariant]
       (φ : D →* MulAut N) (ι : N →* G) (κ : D →* G)
       (hc : ∀ d n, ι (φ d n) = κ d * ι n * (κ d)⁻¹)
       (hφ : ∀ d, MeasurePreserving (φ d) μ μ)
       (actionQ : D →* MulAut Q) (act : G →* Equiv.Perm Q)
       (hact : ∀ u d q, act (ι u * κ d) q = π u * actionQ d q)
       (scale : ℕ → ℝ) (hscale : Tendsto scale atTop atTop) (hscale0 : ∀ n, 0 < scale n)
       (P₂ : ℝ) (R : MeasuredProbeRegions π μQ μI ν scale P₂)
   …

   Mentions: OAI.PolycyclicRecognition.MeasuredProbeRegions