Mathesis

d = 1 universality: every VC-1 class compresses at kernel size one, with no side information. No finiteness, no distinguished member, no chain hypothesis. Twist the class by any member to place ∅ in it; there the VC bound makes co-member points comparable in the membership order, so every label set is a finite chain; anchor at its maximum, reconstruct with interConvention, and transport the scheme back with the same kernels.

DeclStructuralIgnorance.hasKernelScheme_one_of_vcBounded_one
∀ {α : Type u_1} [inst : DecidableEq α] {𝒜 : Set (Set α)},
  StructuralIgnorance.vcBounded 𝒜 1 → StructuralIgnorance.HasKernelScheme 𝒜 1

Arguments

DOIAuthorDate
MTH.R-2026-6025Dhruv GuptaDhruv Gupta2026-09-24T00:00:00Z
DOIMTH.C-2026-6025
Cite

Verification

Library
ZPM.Measurements.SI.DefectTwist.VCOne
Statement digest
6f00e0db8508
First verified
2026-09-24T00:00:00Z