Chern--Simons set identification conjecture for negative definite plumbed manifolds

Let MM be the plumbed 33-manifold in the preceding asymptotic expansion, let S\mathcal{S} be the finite set of phases appearing there, and let CSC(M)\operatorname{CS}_{\mathbb{C}}(M) be the set of Chern--Simons invariants of MM. Chern--Simons set identification conjecture. The finite set S\mathcal{S} coincides with

CSC(M){0}.\operatorname{CS}_{\mathbb{C}}(M)\cup\{0\}.

This conjecture compares the phases obtained analytically from the plumbing formula with the Chern--Simons spectrum predicted by Witten's asymptotic expansion conjecture. The source gives no resolution status.

Sources & referencesView supporting material

Primary source

Yuya Murakami, “A framework for proving quantum modularity: Application to Witten's asymptotic expansion conjecture”, arXiv:2508.21710 (2025).

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