Variational Backbone and Regime Closures XIII: Gauge Forces as Operator Instances and RG Readouts Yang–Mills principal operator and asymptotic freedom as a scale-instance output

Key Points

• This research aims to analyze gauge forces as operator instances within a variational backbone framework, focusing on logarithmic running and asymptotic freedom.
• Placed gauge forces as operator instances on a variational backbone
• Analyzed logarithmic running and asymptotic freedom at the scale-instance level
• Defined a canonical Yang–Mills principal-operator normal form
• Separated principal-operator invariant changes from RG readouts
• Established the role of gauge forces within a fixed variational framework
• Identified the importance of logarithmic running and asymptotic freedom at scale-instance levels
• Clarified distinctions between principal-operator invariant changes and RG readouts