Improved integrality of Donaldson–Thomas invariants of loop quivers (GKS Conjecture 1.3 for twist knots)

Lineage and corrections

This event attributed to Claude Fable 5

Basor, Conrey, Morrison - Knots and ones (the earlier m=3 / figure-eight case) evidence for this event

Improved integrality of Donaldson–Thomas invariants of loop quivers (GKS Conjecture 1.3 for twist knots) parent of this event

The sharp valuation bounds and optimal $\gamma(m)$ are proved for ALL loop quivers $m\ge2$, hence for the extremal BPS invariants of all twist knots (both rows, matching every twist-knot entry of GKS Table 1). Scope limits: the $m=3$/figure-eight divisibility $2n_r/r\in\mathbb Z$ was previously proved by Basor–Conrey–Morrison (arXiv:1703.00990), whose per-$r$ $2$-adic characterization for $m=3$ is finer than the uniform bound; the torus-knot case of GKS Conj. 1.3 (multi-vertex quivers, $\gamma$ growing with the knot) remains open and is not claimed; the general-knot conjecture remains open. The Lean formalization covers the reduction to the classical Kazandzidis congruences, not those congruences themselves. parent of this event

Garoufalidis, Kucharski, Sułkowski - Knots, BPS states, and algebraic curves (Conjecture 1.3) evidence for this event

Improved integrality of Donaldson–Thomas invariants of loop quivers (GKS Conjecture 1.3 for twist knots) evidence for this event

VibeMathed record: Improved integrality of Donaldson–Thomas invariants of loop quivers (GKS Conjecture 1.3 for twist knots) evidence for this event