Unconditional AAK theorem from the affine-pullback stable collar #
The exact relative stable-collar construction supplies the stable homotopy-invariance input required
by the refined S6 route. This module provides the final adapter and exports the arbitrary-
n fair-partition theorem without a theorem-provider argument.
theorem
NRR.AAK.avvakumov_akopyan_karasev
(K : Geometry.ConvexBody Geometry.Plane)
(n : ℕ)
:
0 < n → ∃ (P : ConvexPartition K n), P.IsFair
Unconditional arbitrary-n Akopyan--Avvakumov--Karasev theorem obtained from the concrete
affine-pullback collar, Route B perturbation, finite Stokes comparison, and the stable refined S6
obstruction.
theorem
NRR.avvakumov_akopyan_karasev
(K : Geometry.ConvexBody Geometry.Plane)
(n : ℕ)
:
0 < n → ∃ (P : ConvexPartition K n), P.IsFair
Canonical top-level public theorem. The conditional theorem-provider form is available as
avvakumov_akopyan_karasev_of_primeRefinement.
theorem
NRR.avvakumov_akopyan_karasev_affinePullback
(K : Geometry.ConvexBody Geometry.Plane)
(n : ℕ)
:
0 < n → ∃ (P : ConvexPartition K n), P.IsFair
Route-specific alias for the unconditional affine-pullback proof.