Undirected DJ gap. Already available: equality of graphon classes, hom densities, all finite sample laws, infinite laws, and cut distance zero. Not yet packaged/proved in the exact DJ Theorem 7.1 form — two separate clauses (per review, to be distinguished, not merged):
- equality after common measure-preserving pullbacks (the coupling clause:
W₁ ∘ φ₁ = W₂ ∘ φ₂ a.e. for a common pair of MP maps);
- equality through an auxiliary product-space map (the auxiliary-variable / Aldous–Hoover clause — a different construction, not derivable by renaming the first).
Strong overlap with #74 (pure graphons — its Theorem 13.10 coupling material); coordinate the two rather than duplicating.
Undirected DJ gap. Already available: equality of graphon classes, hom densities, all finite sample laws, infinite laws, and cut distance zero. Not yet packaged/proved in the exact DJ Theorem 7.1 form — two separate clauses (per review, to be distinguished, not merged):
W₁ ∘ φ₁ = W₂ ∘ φ₂a.e. for a common pair of MP maps);Strong overlap with #74 (pure graphons — its Theorem 13.10 coupling material); coordinate the two rather than duplicating.