The paper claims that at hybrid exceptional-diabolic points in a four-mode bosonic system, the quantum Fisher information diverges as theta^{-4}, giving a quadratic error scaling delta-theta proportional to theta^2 that doubles the scaling exponent of ordinary singularities.
Kato, Perturbation Theory for Linear Operators (Springer, 1966)
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Enhanced quantum sensing with hybrid exceptional-diabolic singularities
The paper claims that at hybrid exceptional-diabolic points in a four-mode bosonic system, the quantum Fisher information diverges as theta^{-4}, giving a quadratic error scaling delta-theta proportional to theta^2 that doubles the scaling exponent of ordinary singularities.