ABC

Claim: complete proof of the ABC conjecture.
Key step: a self-adjoint resonance operator and its principal trace inequality force
c<Rad⁡(abc) 1+ε\displaystyle c < \operatorname{Rad}(abc)^{\,1+\varepsilon}c<Rad(abc)1+ε for every ε>0\varepsilon>0ε>0.
What to check first: Lemma 4.2 (pp. 7 – 9) — that’s where the spectral-gap estimate lives.
Notebooks and numerical checks will be posted shortly.