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This lecture by VÃctor Enguita Vileta from IFT Madrid explores an alternative approach to understanding the Higgs potential parameters that defy conventional expectations. Discover how near-criticality—a common feature in many dynamical systems—might explain why these parameters appear to be close to critical values marking quantum phase transitions. Learn about the hypothesis that these unexpected parameter values were established by dynamical mechanisms in the Early Universe. Examine the requirements for Beyond the Standard Model (BSM) physics that could provide viable solutions to the Electroweak hierarchy problem through the "Higgs metastability bound." Follow the analysis of two proof-of-concept examples with promising BSM components: the Majoron completion of the Type-I Seesaw mechanism and an axion-like particle (ALP). See how the parametric regions that successfully address the problem overlap significantly with sensitivity regions at next-generation colliders.