The order in the constant-distance branch has denominator dividing the Weyl group
DisprovedHarmonicBuildingKL.constantDistanceOrderDenominatorWDRetired 2026-09-07 — disproved, false as formalized. Do not use as a dependency.
The defect is in the shared definition layer, not in the mathematics of Breiner--Dees. IsPlanarKSHarmonicOn (Def_frame_2026_harmonic_building_conical) is defined purely through Lebesgue integrals -- ksEnergy, ksApproxEnergy, IsKSSobolevOn, SameKSTraceOnCircle -- and, unlike the goal-level predicate IsKSHarmonic, it does not require ContinuousOn. An a.e.-constant map therefore qualifies as "harmonic", and altering a map on a Lebesgue-null, dilation-invariant set (a ray) preserves every hypothesis -- IsHomogeneousOfOrderOn and NonconstantOn included, both being pointwise -- while destroying the pointwise conclusion. The same gap admits order alpha = 0 for nonconstant maps, which the source excludes.
A faithful restatement needs Continuous h (or the conclusion attached to the continuous representative) together with 0 < alpha. No corrected replacement node exists yet.
import Definitions.Def_euclidean_building_directions import Definitions.Def_frame_2026_harmonic_building_conical import Definitions.Def_spherical_great_circle
namespace HarmonicBuildingKL
open HarmonicBuilding EuclideanBuildingDirections
universe v
theorem constantDistanceOrderDenominatorWD
{N : ℕ} (C : EuclideanCoxeterData N) (M : ConicalBuildingModel.{v} N C)
(BM : BuildingWithDirections N C M.carrier)
(h : ℂ → M.carrier) (alpha L : ℝ)
(hhom : IsHomogeneousOfOrderOn M Set.univ h 0 alpha)
(hharm : IsPlanarKSHarmonicOn Set.univ h)
(hnc : NonconstantOn h Set.univ)
(hconst : ∀ theta : ℝ, dist (h (circlePoint 0 1 theta)) (h 0) = L)
(hlen : unitCircleImageLength h = ENNReal.ofReal (2 * Real.pi * alpha * L)) :
∃ m k : ℕ, 0 < m ∧ 0 < k ∧
k ∣ Fintype.card C.weyl ∧ alpha = (m : ℝ) / (k : ℝ) := by sorry
end HarmonicBuildingKL