Equivalence between ζ_MVZ-superheaviness and cohomological superheaviness

Determine whether ζ_MVZ-superheaviness of a compact subset A ⊂ T^*M implies cohomological superheaviness, namely whether the morphism β μ_M: 𝕜_{M×[0,∞)} → ι_A^* 𝕜_{M×[0,∞)} ⊗ or_{M×ℝ}[n] is non-zero in h𝒯_∞(T^*M) whenever A is ζ_MVZ-superheavy.

Background

The paper defines cohomologically superheavy subsets via a non-vanishing condition on a morphism involving the fundamental class μ_M and the projector ι_A^*. It proves that cohomological superheaviness implies ζ_MVZ-superheaviness, and shows that the Viterbo conjecture ensures the converse for ζ_MVZ-heavy sets.

However, in general the converse implication (ζ_MVZ-superheavy ⇒ cohomologically superheavy) is unresolved. Establishing this equivalence would unify the microlocal sheaf-theoretic notion of superheaviness with its cohomological characterization.